@unpublished{AlsaedyTarkhanov2016, author = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich}, title = {A Hilbert boundary value problem for generalised Cauchy-Riemann equations}, volume = {5}, number = {1}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-86109}, pages = {21}, year = {2016}, abstract = {We elaborate a boundary Fourier method for studying an analogue of the Hilbert problem for analytic functions within the framework of generalised Cauchy-Riemann equations. The boundary value problem need not satisfy the Shapiro-Lopatinskij condition and so it fails to be Fredholm in Sobolev spaces. We show a solvability condition of the Hilbert problem, which looks like those for ill-posed problems, and construct an explicit formula for approximate solutions.}, language = {en} } @unpublished{AlsaedyTarkhanov2013, author = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich}, title = {Normally solvable nonlinear boundary value problems}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-65077}, year = {2013}, abstract = {We study a boundary value problem for an overdetermined elliptic system of nonlinear first order differential equations with linear boundary operators. Such a problem is solvable for a small set of data, and so we pass to its variational formulation which consists in minimising the discrepancy. The Euler-Lagrange equations for the variational problem are far-reaching analogues of the classical Laplace equation. Within the framework of Euler-Lagrange equations we specify an operator on the boundary whose zero set consists precisely of those boundary data for which the initial problem is solvable. The construction of such operator has much in common with that of the familiar Dirichlet to Neumann operator. In the case of linear problems we establish complete results.}, language = {en} } @unpublished{Anders2009, author = {Anders, Martin}, title = {Martingale, Amarts und das starke Gesetz der Grossen Zahlen}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49494}, year = {2009}, abstract = {Aus dem Inhalt: Einleitung Kapitel 1. Starke Gesetze der Grossen Zahlen 1. SGGZ unter Wachstumsbedingungen an die p-ten Momente 2. SGGZ f{\"u}r identisch verteilte Zufallsvariablen 3. SGGZ f{\"u}r Prozesse mit *-mixing-Eigenschaft Kapitel 2. Einf{\"u}hrung zu diskreten (Sub-,Super-)Martingalen 1. Vorhersagbarkeit 2. gestoppte (Sub-,Super-)Martingale 3. Upcrossings 4. Konvergenzs{\"a}tze 5. Doob-Zerlegung 6. Eine {\"a}quivalente Definition eines (Sub-)Martingals Kapitel 3. Martingale und gleichgradige Integrierbarkeit 1. Gleichm{\"a}ßige(-f¨ormige,-gradige) Integrierbarkeit 2. gleichgradig integrierbare Martingale Kapitel 4. Martingale und das SGGZ Kapitel 5."reversed" (Sub-,Super-)Martingale 1. Konvergenzs{\"a}tze Kapitel 6. (Sub-,Super-)Martingale mit gerichteter Indexmenge 1. {\"A}quivalente Formulierung eines (Sub-)Martingals 2. Konvergenzs{\"a}tze Kapitel 7. Quasimartingale,Amarts und Semiamarts 1. Konvergenzs{\"a}tze 2. Riesz-Zerlegung 3. Doob-Zerlegung Kapitel 8. Amarts und das SGGZ Kapitel 9."reversed" Amarts und Semiamarts 1. Konvergenzs{\"a}tze 2."Aufw{\"a}rts"- gegen "Abw{\"a}rts"-Adaptiertheit 3. Riesz-Zerlegung 4. Stabilit{\"a}tsanalyse Kapitel 10. Amarts mit gerichteter Indexmenge 1. Konvergenzs{\"a}tze 2. Riesz-Zerlegung Anhang A. zur Existenz einer Folge unabh{\"a}ngiger Zufallsvariablen B. Konvergenz}, language = {de} } @unpublished{AntonioukKiselevStepanenkoetal.2012, author = {Antoniouk, Alexandra Viktorivna and Kiselev, Oleg and Stepanenko, Vitaly and Tarkhanov, Nikolai Nikolaevich}, title = {Asymptotic solutions of the Dirichlet problem for the heat equation at a characteristic point}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-61987}, year = {2012}, abstract = {The Dirichlet problem for the heat equation in a bounded domain is characteristic, for there are boundary points at which the boundary touches a characteristic hyperplane t = c, c being a constant. It was I.G. Petrovskii (1934) who first found necessary and sufficient conditions on the boundary which guarantee that the solution is continuous up to the characteristic point, provided that the Dirichlet data are continuous. This paper initiated standing interest in studying general boundary value problems for parabolic equations in bounded domains. We contribute to the study by constructing a formal solution of the Dirichlet problem for the heat equation in a neighbourhood of a characteristic boundary point and showing its asymptotic character.}, language = {en} } @unpublished{BagderinaTarkhanov2013, author = {Bagderina, Yulia Yu. and Tarkhanov, Nikolai Nikolaevich}, title = {Differential invariants of a class of Lagrangian systems with two degrees of freedom}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-63129}, year = {2013}, abstract = {We consider systems of Euler-Lagrange equations with two degrees of freedom and with Lagrangian being quadratic in velocities. For this class of equations the generic case of the equivalence problem is solved with respect to point transformations. Using Lie's infinitesimal method we construct a basis of differential invariants and invariant differentiation operators for such systems. We describe certain types of Lagrangian systems in terms of their invariants. The results are illustrated by several examples.}, language = {en} } @unpublished{BagdonavičiusLevulieneNikulinetal.2004, author = {Bagdonavičius, Vilijandas B. and Levuliene, Ruta and Nikulin, Mikhail S. and Zdorova-Cheminade, Olga}, title = {Tests for homogeneity of survival distributions against non-location alternatives and analysis of the gastric cancer data}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51527}, year = {2004}, abstract = {The two and k-sample tests of equality of the survival distributions against the alternatives including cross-effects of survival functions, proportional and monotone hazard ratios, are given for the right censored data. The asymptotic power against approaching alternatives is investigated. The tests are applied to the well known chemio and radio therapy data of the Gastrointestinal Tumor Study Group. The P-values for both proposed tests are much smaller then in the case of other known tests. Differently from the test of Stablein and Koutrouvelis the new tests can be applied not only for singly but also to randomly censored data.}, language = {en} } @unpublished{BermanTarkhanov2004, author = {Berman, Gennady and Tarkhanov, Nikolai Nikolaevich}, title = {Quantum dynamics in the Fermi-Pasta-Ulam problem}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26695}, year = {2004}, abstract = {We study the dynamics of four wave interactions in a nonlinear quantum chain of oscillators under the "narrow packet" approximation. We determine the set of times for which the evolution of decay processes is essentially specified by quantum effects. Moreover, we highlight the quantum increment of instability.}, language = {en} } @unpublished{BlanchardDelattreRoquain2012, author = {Blanchard, Gilles and Delattre, Sylvain and Roquain, {\´E}tienne}, title = {Testing over a continuum of null hypotheses}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-56877}, year = {2012}, abstract = {We introduce a theoretical framework for performing statistical hypothesis testing simultaneously over a fairly general, possibly uncountably infinite, set of null hypotheses. This extends the standard statistical setting for multiple hypotheses testing, which is restricted to a finite set. This work is motivated by numerous modern applications where the observed signal is modeled by a stochastic process over a continuum. As a measure of type I error, we extend the concept of false discovery rate (FDR) to this setting. The FDR is defined as the average ratio of the measure of two random sets, so that its study presents some challenge and is of some intrinsic mathematical interest. Our main result shows how to use the p-value process to control the FDR at a nominal level, either under arbitrary dependence of p-values, or under the assumption that the finite dimensional distributions of the p-value process have positive correlations of a specific type (weak PRDS). Both cases generalize existing results established in the finite setting, the latter one leading to a less conservative procedure. The interest of this approach is demonstrated in several non-parametric examples: testing the mean/signal in a Gaussian white noise model, testing the intensity of a Poisson process and testing the c.d.f. of i.i.d. random variables. Conceptually, an interesting feature of the setting advocated here is that it focuses directly on the intrinsic hypothesis space associated with a testing model on a random process, without referring to an arbitrary discretization.}, language = {en} } @unpublished{BlanchardKraemer2016, author = {Blanchard, Gilles and Kr{\"a}mer, Nicole}, title = {Convergence rates of kernel conjugate gradient for random design regression}, volume = {5}, number = {8}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-94195}, pages = {31}, year = {2016}, abstract = {We prove statistical rates of convergence for kernel-based least squares regression from i.i.d. data using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is related to Kernel Partial Least Squares, a regression method that combines supervised dimensionality reduction with least squares projection. Following the setting introduced in earlier related literature, we study so-called "fast convergence rates" depending on the regularity of the target regression function (measured by a source condition in terms of the kernel integral operator) and on the effective dimensionality of the data mapped into the kernel space. We obtain upper bounds, essentially matching known minimax lower bounds, for the L^2 (prediction) norm as well as for the stronger Hilbert norm, if the true regression function belongs to the reproducing kernel Hilbert space. If the latter assumption is not fulfilled, we obtain similar convergence rates for appropriate norms, provided additional unlabeled data are available.}, language = {en} } @unpublished{BlanchardMathe2012, author = {Blanchard, Gilles and Math{\´e}, Peter}, title = {Discrepancy principle for statistical inverse problems with application to conjugate gradient iteration}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-57117}, year = {2012}, abstract = {The authors discuss the use of the discrepancy principle for statistical inverse problems, when the underlying operator is of trace class. Under this assumption the discrepancy principle is well defined, however a plain use of it may occasionally fail and it will yield sub-optimal rates. Therefore, a modification of the discrepancy is introduced, which takes into account both of the above deficiencies. For a variety of linear regularization schemes as well as for conjugate gradient iteration this modification is shown to yield order optimal a priori error bounds under general smoothness assumptions. A posteriori error control is also possible, however at a sub-optimal rate, in general. This study uses and complements previous results for bounded deterministic noise.}, language = {en} } @unpublished{BlanchardMuecke2016, author = {Blanchard, Gilles and M{\"u}cke, Nicole}, title = {Optimal rates for regularization of statistical inverse learning problems}, volume = {5}, number = {5}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-89782}, pages = {36}, year = {2016}, abstract = {We consider a statistical inverse learning problem, where we observe the image of a function f through a linear operator A at i.i.d. random design points X_i, superposed with an additional noise. The distribution of the design points is unknown and can be very general. We analyze simultaneously the direct (estimation of Af) and the inverse (estimation of f) learning problems. In this general framework, we obtain strong and weak minimax optimal rates of convergence (as the number of observations n grows large) for a large class of spectral regularization methods over regularity classes defined through appropriate source conditions. This improves on or completes previous results obtained in related settings. The optimality of the obtained rates is shown not only in the exponent in n but also in the explicit dependence of the constant factor in the variance of the noise and the radius of the source condition set.}, language = {en} } @unpublished{BrauerKarp2006, author = {Brauer, Uwe and Karp, Lavi}, title = {Local existence of classical solutions for the Einstein-Euler system using weighted Sobolev spaces of fractional order}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30175}, year = {2006}, abstract = {We prove the existence of a class of local in time solutions, including static solutions, of the Einstein-Euler system. This result is the relativistic generalisation of a similar result for the Euler-Poisson system obtained by Gamblin [8]. As in his case the initial data of the density do not have compact support but fall off at infinity in an appropriate manner. An essential tool in our approach is the construction and use of weighted Sobolev spaces of fractional order. Moreover, these new spaces allow us to improve the regularity conditions for the solutions of evolution equations. The details of this construction, the properties of these spaces and results on elliptic and hyperbolic equations will be presented in a forthcoming article.}, language = {en} } @unpublished{BrauerKarp2008, author = {Brauer, Uwe and Karp, Lavi}, title = {Well-posedness of Einstein-Euler systems in asymptotically flat spacetimes}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30347}, year = {2008}, abstract = {We prove a local in time existence and uniqueness theorem of classical solutions of the coupled Einstein{Euler system, and therefore establish the well posedness of this system. We use the condition that the energy density might vanish or tends to zero at infinity and that the pressure is a certain function of the energy density, conditions which are used to describe simplified stellar models. In order to achieve our goals we are enforced, by the complexity of the problem, to deal with these equations in a new type of weighted Sobolev spaces of fractional order. Beside their construction, we develop tools for PDEs and techniques for hyperbolic and elliptic equations in these spaces. The well posedness is obtained in these spaces.}, language = {en} } @unpublished{BuchholzSchulze1998, author = {Buchholz, Thilo and Schulze, Bert-Wolfgang}, title = {Volterra operators and parabolicity : anisotropic pseudo-differential operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25231}, year = {1998}, abstract = {Parabolic equations on manifolds with singularities require a new calculus of anisotropic pseudo-differential operators with operator-valued symbols. The paper develops this theory along the lines of sn abstract wedge calculus with strongly continuous groups of isomorphisms on the involved Banach spaces. The corresponding pseodo-diferential operators are continuous in anisotropic wedge Sobolev spaces, and they form an alegbra. There is then introduced the concept of anisotropic parameter-dependent ellipticity, based on an order reduction variant of the pseudo-differential calculus. The theory is appled to a class of parabolic differential operators, and it is proved the invertibility in Sobolev spaces with exponential weights at infinity in time direction.}, language = {en} } @unpublished{Baer2012, author = {B{\"a}r, Christian}, title = {Renormalized integrals and a path integral formula for the heat kernel on a manifold}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-60052}, year = {2012}, abstract = {We introduce renormalized integrals which generalize conventional measure theoretic integrals. One approximates the integration domain by measure spaces and defines the integral as the limit of integrals over the approximating spaces. This concept is implicitly present in many mathematical contexts such as Cauchy's principal value, the determinant of operators on a Hilbert space and the Fourier transform of an L^p function. We use renormalized integrals to define a path integral on manifolds by approximation via geodesic polygons. The main part of the paper is dedicated to the proof of a path integral formula for the heat kernel of any self-adjoint generalized Laplace operator acting on sections of a vector bundle over a compact Riemannian manifold.}, language = {en} } @unpublished{Baer2012, author = {B{\"a}r, Christian}, title = {Some properties of solutions to weakly hypoelliptic equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-60064}, year = {2012}, abstract = {A linear differential operator L is called weakly hypoelliptic if any local solution u of Lu = 0 is smooth. We allow for systems, i.e. the coefficients may be matrices, not necessarily of square size. This is a huge class of important operators which covers all elliptic, overdetermined elliptic, subelliptic and parabolic equations. We extend several classical theorems from complex analysis to solutions of any weakly hypoelliptic equation: the Montel theorem providing convergent subsequences, the Vitali theorem ensuring convergence of a given sequence, and Riemann's first removable singularity theorem. In the case of constant coefficients we show that Liouville's theorem holds, any bounded solution must be constant and any L^p solution must vanish.}, language = {en} } @unpublished{BaerBallmann2012, author = {B{\"a}r, Christian and Ballmann, Werner}, title = {Boundary value problems for elliptic differential operators of first order}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-60023}, year = {2012}, abstract = {We study boundary value problems for linear elliptic differential operators of order one. The underlying manifold may be noncompact, but the boundary is assumed to be compact. We require a symmetry property of the principal symbol of the operator along the boundary. This is satisfied by Dirac type operators, for instance. We provide a selfcontained introduction to (nonlocal) elliptic boundary conditions, boundary regularity of solutions, and index theory. In particular, we simplify and generalize the traditional theory of elliptic boundary value problems for Dirac type operators. We also prove a related decomposition theorem, a general version of Gromov and Lawson's relative index theorem and a generalization of the cobordism theorem.}, language = {en} } @unpublished{BaerGinoux2012, author = {B{\"a}r, Christian and Ginoux, Nicolas}, title = {Classical and quantum fields on Lorentzian manifolds}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-59973}, year = {2012}, abstract = {We construct bosonic and fermionic locally covariant quantum fields theories on curved backgrounds for large classes of fields. We investigate the quantum field and n-point functions induced by suitable states.}, language = {en} } @unpublished{BaerPfaeffle2012, author = {B{\"a}r, Christian and Pf{\"a}ffle, Frank}, title = {Wiener measures on Riemannian manifolds and the Feynman-Kac formula}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-59998}, year = {2012}, abstract = {This is an introduction to Wiener measure and the Feynman-Kac formula on general Riemannian manifolds for Riemannian geometers with little or no background in stochastics. We explain the construction of Wiener measure based on the heat kernel in full detail and we prove the Feynman-Kac formula for Schr{\"o}dinger operators with bounded potentials. We also consider normal Riemannian coverings and show that projecting and lifting of paths are inverse operations which respect the Wiener measure.}, language = {en} } @unpublished{BoeckmannBieleNeuberetal.1997, author = {B{\"o}ckmann, Christine and Biele, Jens and Neuber, Roland and Niebsch, Jenny}, title = {Retrieval of multimodal aerosol size distribution by inversion of multiwavelength data}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14360}, year = {1997}, abstract = {The ill-posed problem of aerosol size distribution determination from a small number of backscatter and extinction measurements was solved successfully with a mollifier method which is advantageous since the ill-posed part is performed on exactly given quantities, the points r where n(r) is evaluated may be freely selected. A new twodimensional model for the troposphere is proposed.}, language = {en} } @unpublished{BoeckmannNiebsch1998, author = {B{\"o}ckmann, Christine and Niebsch, Jenny}, title = {Examination of the nonlinear LIDAR-operator : the influence of inhomogeneous absorbing spheres on the operator}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14725}, year = {1998}, abstract = {The determination of the atmospheric aerosol size distribution is an inverse illposed problem. The shape and the material composition of the air-carried particles are two substantial model parameters. Present evaluation algorithms only used an approximation with spherical homogeneous particles. In this paper we propose a new numerically efficient recursive algorithm for inhomogeneous multilayered coated and absorbing particles. Numerical results of real existing particles show that the influence of the two parameters on the model is very important and therefore cannot be ignored.}, language = {en} } @unpublished{BoeckmannSarkoezi1999, author = {B{\"o}ckmann, Christine and Sark{\"o}zi, Janos}, title = {The ill-posed inversion of multiwavelength lidar data by a hybrid method of variable projection}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14847}, year = {1999}, abstract = {The ill-posed problem of aerosol distribution determination from a small number of backscatter and extinction lidar measurements was solved successfully via a hybrid method by a variable dimension of projection with B-Splines. Numerical simulation results with noisy data at different measurement situations show that it is possible to derive a reconstruction of the aerosol distribution only with 4 measurements.}, language = {en} } @unpublished{CalinDerChen2004, author = {Calin, Ovidium and Der-Chen, Chang}, title = {The geometry on a step 3 Grushin model}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26724}, year = {2004}, abstract = {In this article we study the geometry associated with the sub-elliptic operator ½ (X²1 +X²2), where X1 = ∂x and X2 = x²/2 ∂y are vector fields on R². We show that any point can be connected with the origin by at least one geodesic and we provide an approximate formula for the number of the geodesics between the origin and the points situated outside of the y-axis. We show there are in¯nitely many geodesics between the origin and the points on the y-axis.}, language = {en} } @unpublished{CalvoSchulze2005, author = {Calvo, D. and Schulze, Bert-Wolfgang}, title = {Operators on corner manifolds with exit to infinity}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29753}, year = {2005}, abstract = {We study (pseudo-)differential operators on a manifold with edge Z, locally modelled on a wedge with model cone that has itself a base manifold W with smooth edge Y . The typical operators A are corner degenerate in a specific way. They are described (modulo 'lower order terms') by a principal symbolic hierarchy σ(A) = (σ ψ(A), σ ^(A), σ ^(A)), where σ ψ is the interior symbol and σ ^(A)(y, η), (y, η) 2 T*Y \ 0, the (operator-valued) edge symbol of 'first generation', cf. [15]. The novelty here is the edge symbol σ^ of 'second generation', parametrised by (z, Ϛ) 2 T*Z \ 0, acting on weighted Sobolev spaces on the infinite cone with base W. Since such a cone has edges with exit to infinity, the calculus has the problem to understand the behaviour of operators on a manifold of that kind. We show the continuity of corner-degenerate operators in weighted edge Sobolev spaces, and we investigate the ellipticity of edge symbols of second generation. Starting from parameter-dependent elliptic families of edge operators of first generation, we obtain the Fredholm property of higher edge symbols on the corresponding singular infinite model cone.}, language = {en} } @unpublished{CalvoSchulze2005, author = {Calvo, D. and Schulze, Bert-Wolfgang}, title = {Edge symbolic structures of second generation}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29940}, year = {2005}, abstract = {Operators on a manifold with (geometric) singularities are degenerate in a natural way. They have a principal symbolic structure with contributions from the different strata of the configuration. We study the calculus of such operators on the level of edge symbols of second generation, based on specific quantizations of the corner-degenerate interior symbols, and show that this structure is preserved under compositions.}, language = {en} } @unpublished{Camales2003, author = {Camal{\`e}s, Renaud}, title = {A note on the ramified Cauchy problem}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26646}, year = {2003}, abstract = {In this paper, the ramified Cauchy problem in C² for operator with multiple characteristics of constant multiplicity and second member ramified around some analytic set is studied.}, language = {en} } @unpublished{CattiauxDaiPraPoelly2007, author = {Cattiaux, Patrick and Dai Pra, Paolo and Poelly, Sylvie}, title = {A constructive approach to a class of ergodic HJB equations with nonsmooth cost}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49430}, year = {2007}, abstract = {We consider a class of ergodic Hamilton-Jacobi-Bellman (HJB) equations, related to large time asymptotics of non-smooth multiplicative functional of difusion processes. Under suitable ergodicity assumptions on the underlying difusion, we show existence of these asymptotics, and that they solve the related HJB equation in the viscosity sense.}, language = {en} } @unpublished{CattiauxFradonKuliketal.2013, author = {Cattiaux, Patrick and Fradon, Myriam and Kulik, Alexei Michajlovič and Roelly, Sylvie}, title = {Long time behavior of stochastic hard ball systems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-68388}, year = {2013}, abstract = {We study the long time behavior of a system of two or three Brownian hard balls living in the Euclidean space of dimension at least two, submitted to a mutual attraction and to elastic collisions.}, language = {en} } @unpublished{ChampagnatRoelly2007, author = {Champagnat, Nicolas and Roelly, Sylvie}, title = {Limit theorems for conditioned multitype Dawson-Watanabe processes}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49426}, year = {2007}, abstract = {A multitype Dawson-Watanabe process is conditioned, in subcritical and critical cases, on non-extinction in the remote future. On every nite time interval, its distribution law is absolutely continuous with respect to the law of the unconditioned process. A martingale problem characterization is also given. The explicit form of the Laplace functional of the conditioned process is used to obtain several results on the long time behaviour of the mass of the conditioned and unconditioned processes. The general case is considered first, where the mutation matrix which modelizes the interaction between the types, is irreducible. Several two-type models with decomposable mutation matrices are also analysed.}, language = {en} } @unpublished{ChenHidetoshi1998, author = {Chen, Hua and Hidetoshi, Tahara}, title = {On the holomorphic solution of non-linear totally characteristic equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25333}, year = {1998}, abstract = {The paper deals with a non-linear singular partial differential equation: (E) t∂/∂t = F(t, x, u, ∂u/∂x) in the holomorphic category. When (E) is of Fuchsian type, the existence of the unique holomorphic solution was established by G{\´e}rard-Tahara [2]. In this paper, under the assumption that (E) is of totally characteristic type, the authors give a sufficient condition for (E) to have a unique holomorphic solution. The result is extended to higher order case.}, language = {en} } @unpublished{ChenLiLiu2008, author = {Chen, Hua and Li, Jun-Feng and Liu, Wei-An}, title = {Behavior of the solution to a chemotaxis model with reproduction term}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30304}, year = {2008}, abstract = {Contents: 1 Introduction 2 Global existence and blow-up or quenching of the solution 3 Detailed asymptotical behavior of the solution}, language = {en} } @unpublished{ChenLi2007, author = {Chen, Hua and Li, Ke}, title = {The existence and regularity of multiple solutions for a class of infinitely degenerate elliptic equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30247}, year = {2007}, abstract = {Let X = (X1,.....,Xm) be an infinitely degenerate system of vector fields, we study the existence and regularity of multiple solutions of Dirichelt problem for a class of semi-linear infinitely degenerate elliptic operators associated with the sum of square operator Δx = ∑m(j=1) Xj* Xj.}, language = {en} } @unpublished{ChenLiXu2007, author = {Chen, Hua and Li, Wei-Xi and Xu, Chao-Jiang}, title = {Gevrey hypoellipticity for linear and non-linear Fokker-Planck equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30283}, year = {2007}, abstract = {This paper studies the Gevrey regularity of weak solutions of a class of linear and semilinear Fokker-Planck equations.}, language = {en} } @unpublished{ChenLua1998, author = {Chen, Hua and Lua, Zhuangehu}, title = {On the holomorphic solution of non-linear totally characteristic equations with several space variables}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25189}, year = {1998}, abstract = {In this paper we study a class of non-linear singular partial differential equation in complex domain Csub(t) x C n sub(x). Under certain assumptions, we prove the existence and uniqueness of holomorphic solution near origin of Csub(t) x C n sub(x).}, language = {en} } @unpublished{ChenWu2006, author = {Chen, Hua and Wu, Shaohua}, title = {On existence of solutions for some hyperbolic-parabolic type chemotaxis systems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30082}, year = {2006}, abstract = {In this paper, we discuss the local and global existence of week solutions for some hyperbolic-parabolic systems modelling chemotaxis.}, language = {en} } @unpublished{ChenYu2001, author = {Chen, Hua and Yu, Chun}, title = {Asymptotic behaviour of the trace for Schr{\"o}dinger operator on fractal drums}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26157}, year = {2001}, language = {en} } @unpublished{Conforti2015, author = {Conforti, Giovanni}, title = {Reciprocal classes of continuous time Markov Chains}, volume = {4}, number = {8}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-78234}, pages = {198}, year = {2015}, abstract = {In this work we study reciprocal classes of Markov walks on graphs. Given a continuous time reference Markov chain on a graph, its reciprocal class is the set of all probability measures which can be represented as a mixture of the bridges of the reference walks. We characterize reciprocal classes with two different approaches. With the first approach we found it as the set of solutions to duality formulae on path space, where the differential operators have the interpretation of the addition of infinitesimal random loops to the paths of the canonical process. With the second approach we look at short time asymptotics of bridges. Both approaches allow an explicit computation of reciprocal characteristics, which are divided into two families, the loop characteristics and the arc characteristics. They are those specific functionals of the generator of the reference chain which determine its reciprocal class. We look at the specific examples such as Cayley graphs, the hypercube and planar graphs. Finally we establish the first concentration of measure results for the bridges of a continuous time Markov chain based on the reciprocal characteristics.}, language = {en} } @unpublished{ConfortiDaiPraRoelly2014, author = {Conforti, Giovanni and Dai Pra, Paolo and Roelly, Sylvie}, title = {Reciprocal class of jump processes}, volume = {3}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-70776}, pages = {30}, year = {2014}, abstract = {Processes having the same bridges as a given reference Markov process constitute its reciprocal class. In this paper we study the reciprocal class of compound Poisson processes whose jumps belong to a finite set A in R^d. We propose a characterization of the reciprocal class as the unique set of probability measures on which a family of time and space transformations induces the same density, expressed in terms of the reciprocal invariants. The geometry of A plays a crucial role in the design of the transformations, and we use tools from discrete geometry to obtain an optimal characterization. We deduce explicit conditions for two Markov jump processes to belong to the same class. Finally, we provide a natural interpretation of the invariants as short-time asymptotics for the probability that the reference process makes a cycle around its current state.}, language = {en} } @unpublished{ConfortiLeonardMurretal.2014, author = {Conforti, Giovanni and L{\´e}onard, Christian and Murr, R{\"u}diger and Roelly, Sylvie}, title = {Bridges of Markov counting processes : reciprocal classes and duality formulas}, volume = {3}, number = {9}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-71855}, pages = {12}, year = {2014}, abstract = {Processes having the same bridges are said to belong to the same reciprocal class. In this article we analyze reciprocal classes of Markov counting processes by identifying their reciprocal invariants and we characterize them as the set of counting processes satisfying some duality formula.}, language = {en} } @unpublished{ConfortiRoelly2015, author = {Conforti, Giovanni and Roelly, Sylvie}, title = {Reciprocal class of random walks on an Abelian group}, volume = {4}, number = {1}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72604}, pages = {22}, year = {2015}, abstract = {Processes having the same bridges as a given reference Markov process constitute its reciprocal class. In this paper we study the reciprocal class of a continuous time random walk with values in a countable Abelian group, we compute explicitly its reciprocal characteristics and we present an integral characterization of it. Our main tool is a new iterated version of the celebrated Mecke's formula from the point process theory, which allows us to study, as transformation on the path space, the addition of random loops. Thanks to the lattice structure of the set of loops, we even obtain a sharp characterization. At the end, we discuss several examples to illustrate the richness of reciprocal classes. We observe how their structure depends on the algebraic properties of the underlying group.}, language = {en} } @unpublished{CoriascoPanarese2000, author = {Coriasco, Sandro and Panarese, Paolo}, title = {Fourier integral operators defined by classical symbols with exit behaviour}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25896}, year = {2000}, abstract = {We continue the investigation of the calculus of Fourier Integral Operators (FIOs) in the class of symbols with exit behaviour (SG symbols). Here we analyse what happens when one restricts the choice of amplitude and phase functions to the subclass of the classical SG symbols. It turns out that the main composition theorem, obtained in the environment of general SG classes, has a "classical" counterpart. As an application, we study the Cauchy problem for classical hyperbolic operators of order (1, 1); for such operators we refine the known results about the analogous problem for general SG hyperbolic operators. The material contained here will be used in a forthcoming paper to obtain a Weyl formula for a class of operators defined on manifolds with cylindrical ends, improving the results obtained in [9].}, language = {en} } @unpublished{CoriascoSchroheSeiler2001, author = {Coriasco, Sandro and Schrohe, Elmar and Seiler, J{\"o}rg}, title = {Bounded imaginary powers of differential operators on manifolds with conical singularities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25962}, year = {2001}, abstract = {We study the minimal and maximal closed extension of a differential operator A on a manifold B with conical singularities, when A acts as an unbounded operator on weighted Lp-spaces over B,1 < p < ∞. Under suitable ellipticity assumptions we can define a family of complex powers A up(z), z ∈ C. We also obtain sufficient information on the resolvent of A to show the boundedness of the pure imaginary powers. Examples concern unique solvability and maximal regularity of the solution of the Cauchy problem u' - Δu = f, u(0) = 0, for the Laplacian on conical manifolds.}, language = {en} } @unpublished{CoriascoSchulze2002, author = {Coriasco, Sandro and Schulze, Bert-Wolfgang}, title = {Edge problems on configurations with model cones of different dimensions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26438}, year = {2002}, abstract = {Elliptic equations on configurations W = W1 ∪ ... ∪ Wn with edge Y and components Wj of different dimension can be treated in the frame of pseudo-differential analysis on manifolds with geometric singularities, here, edges. Starting from edge-degenerate operators on Wj, j = 1, ..., N, we construct an algebra with extra "transmission" conditions on Y that satisfy an analogue of the Shapiro-Lopatinskij condition. Ellipticity refers to a two-component symbolic hierarchy with an interior and an edge part; the latter one is operator-valued, operating on the union of different dimensional model cones. We construct parametrices within our calculus, where exchange of information between the various components is encoded in Green and Mellin operators that are smoothing on W\Y. Moreover, we obtain regularity of solutions in weighted edge spaces with asymptotics.}, language = {en} } @unpublished{Davis2002, author = {Davis, Simon}, title = {On the absence of large-order divergences in superstring theory}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26452}, year = {2002}, abstract = {The genus-dependence of multi-loop superstring ams is estimated at large orders in perturbation theory using the super-Schottky group parameterization of supermoduli space. Restriction of the integration region to a subset of supermoduli space and a single fundamental domain of the super-modular group suggests an exponential dependence on the genus. Upper bounds for these estimates are obtained for arbitrary N-point superstring scattering amplitudes and are shown to be consistent with exact results obtained for special type II string amplitudes for orbifold or Calabi-Yau compactifications. The genus-dependence is then obtained by considering the effect of the remaining contribution to the superstring amplitudes after the coefficients of the formally divergent parts of the integrals vanish as a result of a sum over spin structures. The introduction of supersymmetry therefore leads to the elimination of large-order divergences in string pertubation theory, a result which is based only on the supersymmetric generalization of the polyakov measure and not the gauge group of the string model.}, language = {en} } @unpublished{Davis2002, author = {Davis, Simon}, title = {Connections and generalized gauge transformations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26468}, year = {2002}, abstract = {The derivation of the standard model from a higher-dimensional action suggests a further study of the fibre bundle formulation of gauge theories to determine the variations in the choice of structure group that are allowed in this geometrical setting. The action of transformations on the projection of fibres to their submanifolds are characteristic of theories with fewer gauge vector bosons, and specific examples are given, which may have phenomenological relevance. The spinor space for the three generations of fermions in the standard model is described algebraically.}, language = {en} } @unpublished{Davis2002, author = {Davis, Simon}, title = {On the existence of a non-zero lower bound for the number of Goldbach partitions of an even integer}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26474}, year = {2002}, abstract = {The Goldbach partitions of an even number greater than 2, given by the sums of two prime addends, form the non-empty set for all integers 2n with 2 ≤ n ≤ 2 × 1014. It will be shown how to determine by the method of induction the existence of a non-zero lower bound for the number of Goldbach partitions of all even integers greater than or equal to 4. The proof depends on contour arguments for complex functions in the unit disk.}, language = {en} } @unpublished{Davis2003, author = {Davis, Simon}, title = {The quantum cosmological wavefunction at very early times for a quadratic gravity theory}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26520}, year = {2003}, abstract = {The quantum cosmological wavefunction for a quadratic gravity theory derived from the heterotic string effective action is obtained near the inflationary epoch and during the initial Planck era. Neglecting derivatives with respect to the scalar field, the wavefunction would satisfy a third-order differential equation near the inflationary epoch which has a solution that is singular in the scale factor limit a(t) → 0. When scalar field derivatives are included, a sixth-order differential equation is obtained for the wavefunction and the solution by Mellin transform is regular in the a → 0 limit. It follows that inclusion of the scalar field in the quadratic gravity action is necessary for consistency of the quantum cosmology of the theory at very early times.}, language = {en} } @unpublished{DeDonnoSchulze2003, author = {De Donno, G. and Schulze, Bert-Wolfgang}, title = {Meromorphic symbolic structures for boundary value problems on manifolds with edges}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26570}, year = {2003}, abstract = {We investigate the ideal of Green and Mellin operators with asymtotics for a manifold with edge-corner singularities and boundary which belongs to the structure of parametrices of elliptic boundary value problems on a configuration with corners whose base manifolds have edges.}, language = {en} } @unpublished{DeXingHui2003, author = {De-Xing, Kong and Hui, Yao}, title = {Global exact boundary controllability of a class of quasilinear hyperbolic systems of conservation laws II}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26565}, year = {2003}, abstract = {In this paper, by a new constructive method, the authors reprove the global exact boundary controllability of a class of quasilinear hyperbolic systems of conservation laws with linearly degenerate fields. It is shown that the system with nonlinear boundary conditions is globally exactly boundary controllable in the class of piecewise C¹ functions. In particular, the authors give the optimal control time of the system. Finally, a new application is also given.}, language = {en} } @unpublished{DebusscheHoegeleImkeller2013, author = {Debussche, Arnaud and Hoegele, Michael and Imkeller, Peter}, title = {The dynamics of nonlinear reaction-diffusion equations with small levy noise preface}, series = {Lecture notes in mathematics : a collection of informal reports and seminars}, volume = {2085}, journal = {Lecture notes in mathematics : a collection of informal reports and seminars}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-319-00828-8; 978-3-319-00827-1}, issn = {0075-8434}, pages = {V -- +}, year = {2013}, language = {en} } @unpublished{DebusscheHoegeleImkeller2013, author = {Debussche, Arnaud and H{\"o}gele, Michael and Imkeller, Peter}, title = {The dynamics of nonlinear reaction-diffusion equations with small levy noise}, series = {Lecture notes in mathematics : a collection of informal reports and seminars}, volume = {2085}, journal = {Lecture notes in mathematics : a collection of informal reports and seminars}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-319-00828-8; 978-3-319-00827-1}, issn = {0075-8434}, doi = {10.1007/978-3-319-00828-8_1}, pages = {1 -- 10}, year = {2013}, abstract = {Our primary interest in this book lies in the study of dynamical properties of reaction-diffusion equations perturbed by L{\´e}vy noise of intensity ? in the small noise limit ??0 .}, language = {en} } @unpublished{DenkKrainer2006, author = {Denk, Robert and Krainer, Thomas}, title = {R-Boundedness, pseudodifferential operators, and maximal regularity for some classes of partial differential operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30147}, year = {2006}, abstract = {It is shown that an elliptic scattering operator A on a compact manifold with boundary with operator valued coefficients in the morphisms of a bundle of Banach spaces of class (HT ) and Pisier's property (α) has maximal regularity (up to a spectral shift), provided that the spectrum of the principal symbol of A on the scattering cotangent bundle avoids the right half-plane. This is accomplished by representing the resolvent in terms of pseudodifferential operators with R-bounded symbols, yielding by an iteration argument the R-boundedness of λ(A - λ)-1 in R(λ)≥ τ for some τ ∈ IR. To this end, elements of a symbolic and operator calculus of pseudodifferential operators with R-bounded symbols are introduced. The significance of this method for proving maximal regularity results for partial differential operators is underscored by considering also a more elementary situation of anisotropic elliptic operators on Rd with operator valued coefficients.}, language = {en} } @unpublished{DereudreMazzonettoRoelly2016, author = {Dereudre, David and Mazzonetto, Sara and Roelly, Sylvie}, title = {Exact simulation of Brownian diffusions with drift admitting jumps}, volume = {5}, number = {7}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-91049}, pages = {25}, year = {2016}, abstract = {Using an algorithm based on a retrospective rejection sampling scheme, we propose an exact simulation of a Brownian diffusion whose drift admits several jumps. We treat explicitly and extensively the case of two jumps, providing numerical simulations. Our main contribution is to manage the technical difficulty due to the presence of two jumps thanks to a new explicit expression of the transition density of the skew Brownian motion with two semipermeable barriers and a constant drift.}, language = {en} } @unpublished{DereudreMazzonettoRoelly2015, author = {Dereudre, David and Mazzonetto, Sara and Roelly, Sylvie}, title = {An explicit representation of the transition densities of the skew Brownian motion with drift and two semipermeable barriers}, volume = {4}, number = {9}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-80613}, pages = {23}, year = {2015}, abstract = {In this paper we obtain an explicit representation of the transition density of the one-dimensional skew Brownian motion with (a constant drift and) two semipermeable barriers. Moreover we propose a rejection method to simulate this density in an exact way.}, language = {en} } @unpublished{DereudreRoelly2004, author = {Dereudre, David and Roelly, Sylvie}, title = {Propagation of Gibbsianness for infinite-dimensional gradient Brownian diffusions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51535}, year = {2004}, abstract = {We study the (strong-)Gibbsian character on RZd of the law at time t of an infinitedimensional gradient Brownian diffusion , when the initial distribution is Gibbsian.}, language = {en} } @unpublished{DereudreRoelly2014, author = {Dereudre, David and Roelly, Sylvie}, title = {Path-dependent infinite-dimensional SDE with non-regular drift : an existence result}, volume = {3}, number = {11}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72084}, pages = {27}, year = {2014}, abstract = {We establish in this paper the existence of weak solutions of infinite-dimensional shift invariant stochastic differential equations driven by a Brownian term. The drift function is very general, in the sense that it is supposed to be neither small or continuous, nor Markov. On the initial law we only assume that it admits a finite specific entropy. Our result strongly improves the previous ones obtained for free dynamics with a small perturbative drift. The originality of our method leads in the use of the specific entropy as a tightness tool and on a description of such stochastic differential equation as solution of a variational problem on the path space.}, language = {en} } @unpublished{Dicken1998, author = {Dicken, Volker}, title = {Simultaneous activity and attenuation reconstruction in emission tomography}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14747}, year = {1998}, abstract = {In single photon emission computed tomography (SPECT) one is interested in reconstructing the activity distribution f of some radiopharmaceutical. The data gathered suffer from attenuation due to the tissue density µ. Each imaged slice incorporates noisy sample values of the nonlinear attenuated Radon transform (formular at this place in the original abstract) Traditional theory for SPECT reconstruction treats µ as a known parameter. In practical applications, however, µ is not known, but either crudely estimated, determined in costly additional measurements or plainly neglected. We demonstrate that an approximation of both f and µ from SPECT data alone is feasible, leading to quantitatively more accurate SPECT images. The result is based on nonlinear Tikhonov regularization techniques for parameter estimation problems in differential equations combined with Gauss-Newton-CG minimization.}, language = {en} } @unpublished{DinesHarutjunjanSchulze2003, author = {Dines, Nicoleta and Harutjunjan, Gohar and Schulze, Bert-Wolfgang}, title = {The Zaremba problem in edge Sobolev spaces}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26615}, year = {2003}, abstract = {Mixed elliptic boundary value problems are characterised by conditions which have a jump along an interface of codimension 1 on the boundary. We study such problems in weighted edge Sobolev spaces and show the Fredholm property and the existence of parametrices under additional conditions of trace and potential type on the interface. Our methods from the calculus of boundary value problems on a manifold with edges will be illustrated by the Zaremba problem and other mixed problems for the Laplace operator.}, language = {en} } @unpublished{DinesLiuSchulze2004, author = {Dines, Nicoleta and Liu, X. and Schulze, Bert-Wolfgang}, title = {Edge quantisation of elliptic operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26838}, year = {2004}, abstract = {The ellipticity of operators on a manifold with edge is defined as the bijectivity of the components of a principal symbolic hierarchy σ = (σψ, σ∧), where the second component takes value in operators on the infinite model cone of the local wedges. In general understanding of edge problems there are two basic aspects: Quantisation of edge-degenerate operators in weighted Sobolev spaces, and verifying the elliptcity of the principal edge symbol σ∧ which includes the (in general not explicitly known) number of additional conditions on the edge of trace and potential type. We focus here on these queations and give explicit answers for a wide class of elliptic operators that are connected with the ellipticity of edge boundary value problems and reductions to the boundary. In particular, we study the edge quantisation and ellipticity for Dirichlet-Neumann operators with respect to interfaces of some codimension on a boundary. We show analogues of the Agranovich-Dynin formula for edge boundary value problems, and we establish relations of elliptic operators for different weights, via the spectral flow of the underlying conormal symbols.}, language = {en} } @unpublished{DinesSchulze2003, author = {Dines, Nicoleta and Schulze, Bert-Wolfgang}, title = {Mellin-edge representations of elliptic operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26627}, year = {2003}, abstract = {We construct a class of elliptic operators in the edge algebra on a manifold M with an embedded submanifold Y interpreted as an edge. The ellipticity refers to a principal symbolic structure consisting of the standard interior symbol and an operator-valued edge symbol. Given a differential operator A on M for every (sufficiently large) s we construct an associated operator As in the edge calculus. We show that ellipticity of A in the usual sense entails ellipticity of As as an edge operator (up to a discrete set of reals s). Parametrices P of A then correspond to parametrices Ps of As, interpreted as Mellin-edge representations of P.}, language = {en} } @unpublished{Duduchava1999, author = {Duduchava, Roland}, title = {The Green formula and layer potentials}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25601}, year = {1999}, abstract = {The Green formula is proved for boundary value problems (BVPs), when "basic" operator is arbitrary partial differential operator with variable matrix coefficients and "boundary" operators are quasi-normal with vector-coeficients. If the system possesses the fundamental solution, representation formula for a solution is derived and boundedness properties of participating layer potentials from function spaces on the boundary (Besov, Zygmund spaces) into appropriate weighted function spaces on the inner and the outer domains are established. Some related problems are discussed in conclusion: traces of functions from weighted spaces, traces of potential-type functions, Plemelji formulae,Calder{\´o}n projections, restricted smoothness of the underlying surface and coefficients. The results have essential applications in investigations of BVPs by the potential method, in apriori estimates and in asymptotics of solutions.}, language = {en} } @unpublished{DyachenkoTarkhanov2012, author = {Dyachenko, Evgueniya and Tarkhanov, Nikolai Nikolaevich}, title = {Degeneration of boundary layer at singular points}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-60135}, year = {2012}, abstract = {We study the Dirichlet problem in a bounded plane domain for the heat equation with small parameter multiplying the derivative in t. The behaviour of solution at characteristic points of the boundary is of special interest. The behaviour is well understood if a characteristic line is tangent to the boundary with contact degree at least 2. We allow the boundary to not only have contact of degree less than 2 with a characteristic line but also a cuspidal singularity at a characteristic point. We construct an asymptotic solution of the problem near the characteristic point to describe how the boundary layer degenerates.}, language = {en} } @unpublished{DyachenkoTarkhanov2014, author = {Dyachenko, Evgueniya and Tarkhanov, Nikolai Nikolaevich}, title = {Singular perturbations of elliptic operators}, volume = {3}, number = {1}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-69502}, pages = {21}, year = {2014}, abstract = {We develop a new approach to the analysis of pseudodifferential operators with small parameter 'epsilon' in (0,1] on a compact smooth manifold X. The standard approach assumes action of operators in Sobolev spaces whose norms depend on 'epsilon'. Instead we consider the cylinder [0,1] x X over X and study pseudodifferential operators on the cylinder which act, by the very nature, on functions depending on 'epsilon' as well. The action in 'epsilon' reduces to multiplication by functions of this variable and does not include any differentiation. As but one result we mention asymptotic of solutions to singular perturbation problems for small values of 'epsilon'.}, language = {en} } @unpublished{EgorovKondratievSchulze2004, author = {Egorov, Jurij V. and Kondratiev, V. A. and Schulze, Bert-Wolfgang}, title = {On the completeness of root functions of elliptic boundary problems in a domain with conical points on the boundary}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26773}, year = {2004}, abstract = {Contents: 1 Introduction 2 Definitions 3 Rays of minimal growth 4 Proof of Theorem 2. 5 The growth of the resolvent 6 Proof of Theorem 3. 7 The completeness of root functions 8 Some generalizations}, language = {en} } @unpublished{EgorovKondratievSchulze2001, author = {Egorov, Yu. and Kondratiev, V. and Schulze, Bert-Wolfgang}, title = {On completeness of eigenfunctions of an elliptic operator on a manifold with conical points}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25937}, year = {2001}, abstract = {Contents: 1 Introduction 2 Definitions 3 Rays of minimal growth 4 Completeness of root functions}, language = {en} } @unpublished{ElinShoikhetTarkhanov2015, author = {Elin, Mark and Shoikhet, David and Tarkhanov, Nikolai Nikolaevich}, title = {Analytic semigroups of holomorphic mappings and composition operators}, volume = {4}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-77914}, pages = {30}, year = {2015}, abstract = {In this paper we study the problem of analytic extension in parameter for a semigroup of holomorphic self-mappings of the unit ball in a complex Banach space and its relation to the linear continuous semigroup of composition operators. We also provide a brief review around this topic.}, language = {en} } @unpublished{FangXu2005, author = {Fang, Daoyuan and Xu, Jiang}, title = {Asymptotic behavior of solutions to multidimensional nonisentropic hydrodynamic model for semiconductors}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29767}, year = {2005}, abstract = {In this paper, a global existence result of smooth solutions to the multidimen- sional nonisentropic hydrodynamic model for semiconductors is proved, under the assumption that the initial data is a perturbation of the stationary solutions for the thermal equilibrium state. The resulting evolutionary solutions converge to the stationary solutions in time asymptotically exponentially fast.}, language = {en} } @unpublished{FedchenkoTarkhanov2017, author = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich}, title = {A Rad{\´o} Theorem for the Porous Medium Equation}, series = {Preprints des Instituts f{\"u}r Mathematik der Universit{\"a}t Potsdam}, volume = {6}, journal = {Preprints des Instituts f{\"u}r Mathematik der Universit{\"a}t Potsdam}, number = {1}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-102735}, pages = {12}, year = {2017}, abstract = {We prove that each locally Lipschitz continuous function satisfying the porous medium equation away from the set of its zeroes is actually a weak solution of this equation in the whole domain.}, language = {en} } @unpublished{FedchenkoTarkhanov2014, author = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich}, title = {An index formula for Toeplitz operators}, volume = {3}, number = {12}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72499}, pages = {24}, year = {2014}, abstract = {We prove a Fedosov index formula for the index of Toeplitz operators connected with the Hardy space of solutions to an elliptic system of first order partial differential equations in a bounded domain of Euclidean space with infinitely differentiable boundary.}, language = {en} } @unpublished{FedchenkoTarkhanov2013, author = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich}, title = {A Class of Toeplitz Operators in Several Variables}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-68932}, year = {2013}, abstract = {We introduce the concept of Toeplitz operator associated with the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We characterise those Toeplitz operators which are Fredholm, thus initiating the index theory.}, language = {en} } @unpublished{FedchenkoTarkhanov2016, author = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich}, title = {Boundary value problems for elliptic complexes}, volume = {5}, number = {3}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-86705}, pages = {12}, year = {2016}, abstract = {The aim of this paper is to bring together two areas which are of great importance for the study of overdetermined boundary value problems. The first area is homological algebra which is the main tool in constructing the formal theory of overdetermined problems. And the second area is the global calculus of pseudodifferential operators which allows one to develop explicit analysis.}, language = {en} } @unpublished{Fedosov2006, author = {Fedosov, B.}, title = {On a spectral theorem for deformation quantization}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30161}, year = {2006}, abstract = {We give a construction of an eigenstate for a non-critical level of the Hamiltonian function, and investigate the contribution of Morse critical points to the spectral decomposition. We compare the rigorous result with the series obtained by a perturbation theory. As an example the relation to the spectral asymptotics is discussed.}, language = {en} } @unpublished{Fedosov1999, author = {Fedosov, Boris}, title = {Pseudo-differential operators and deformation quantization}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25651}, year = {1999}, abstract = {Using the Riemannian connection on a compact manifold X, we show that the algebra of classical pseudo-differential operators on X generates a canonical deformation quantization on the cotangent manifold T*X. The corresponding Abelian connection is calculated explicitly in terms of the of the exponential mapping. We prove also that the index theorem for elliptic operators may be obtained as a consequence of the index theorem for deformation quantization.}, language = {en} } @unpublished{Fedosov1997, author = {Fedosov, Boris}, title = {Non-Abelian reduction in deformation quantization}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25101}, year = {1997}, abstract = {We consider a G-invariant star-product algebra A on a symplectic manifold (M,ω) obtained by a canonical construction of deformation quantization. Under assumptions of the classical Marsden-Weinstein theorem we define a reduction of the algebra A with respect to the G-action. The reduced algebra turns out to be isomorphic to a canonical star-product algebra on the reduced phase space B. In other words, we show that the reduction commutes with the canonical G-invariant deformation quantization. A similar statement in the framework of geometric quantization is known as the Guillemin-Sternberg conjecture (by now completely proved).}, language = {en} } @unpublished{Fedosov1998, author = {Fedosov, Boris}, title = {Moduli spaces and deformation quantization in infinite dimensions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25396}, year = {1998}, abstract = {We construct a deformation quantization on an infinite-dimensional symplectic space of regular connections on an SU(2)-bundle over a Riemannian surface of genus g ≥ 2. The construction is based on the normal form thoerem representing the space of connections as a fibration over a finite-dimensional moduli space of flat connections whose fibre is a cotangent bundle of the infinite-dimensional gauge group. We study the reduction with respect to the gauge groupe both for classical and quantum cases and show that our quantization commutes with reduction.}, language = {en} } @unpublished{FedosovSchulzeTarkhanov1999, author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {A general index formula on tropic manifolds with conical points}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25501}, year = {1999}, abstract = {We solve the index problem for general elliptic pseudodifferential operators on toric manifolds with conical points.}, language = {en} } @unpublished{FedosovSchulzeTarkhanov1998, author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {A remark on the index of symmetric operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25169}, year = {1998}, abstract = {We introduce a natural symmetry condition for a pseudodifferential operator on a manifold with cylindrical ends ensuring that the operator admits a doubling across the boundary. For such operators we prove an explicit index formula containing, apart from the Atiyah-Singer integral, a finite number of residues of the logarithmic derivative of the conormal symbol.}, language = {en} } @unpublished{FedosovSchulzeTarkhanov1997, author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {The index of elliptic operators on manifolds with conical points}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25096}, year = {1997}, abstract = {For general elliptic pseudodifferential operators on manifolds with singular points, we prove an algebraic index formula. In this formula the symbolic contributions from the interior and from the singular points are explicitly singled out. For two-dimensional manifolds, the interior contribution is reduced to the Atiyah-Singer integral over the cosphere bundle while two additional terms arise. The first of the two is one half of the 'eta' invariant associated to the conormal symbol of the operator at singular points. The second term is also completely determined by the conormal symbol. The example of the Cauchy-Riemann operator on the complex plane shows that all the three terms may be non-zero.}, language = {en} } @unpublished{FedosovSchulzeTarkhanov1998, author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {The index of higher order operators on singular surfaces}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25127}, year = {1998}, abstract = {The index formula for elliptic pseudodifferential operators on a two-dimensional manifold with conical points contains the Atiyah-Singer integral as well as two additional terms. One of the two is the 'eta' invariant defined by the conormal symbol, and the other term is explicitly expressed via the principal and subprincipal symbols of the operator at conical points. In the preceding paper we clarified the meaning of the additional terms for first-order differential operators. The aim of this paper is an explicit description of the contribution of a conical point for higher-order differential operators. We show that changing the origin in the complex plane reduces the entire contribution of the conical point to the shifted 'eta' invariant. In turn this latter is expressed in terms of the monodromy matrix for an ordinary differential equation defined by the conormal symbol.}, language = {en} } @unpublished{FedosovSchulzeTarkhanov1997, author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {On the index formula for singular surfaces}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25116}, year = {1997}, abstract = {In the preceding paper we proved an explicit index formula for elliptic pseudodifferential operators on a two-dimensional manifold with conical points. Apart from the Atiyah-Singer integral, it contains two additional terms, one of the two being the 'eta' invariant defined by the conormal symbol. In this paper we clarify the meaning of the additional terms for differential operators.}, language = {en} } @unpublished{FedosovSchulzeTarkhanov2003, author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {On index theorem for symplectic orbifolds}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26550}, year = {2003}, abstract = {We give an explicit construction of the trace on the algebra of quantum observables on a symplectic orbifold and propose an index formula.}, language = {en} } @unpublished{FedosovTarkhanov2015, author = {Fedosov, Boris and Tarkhanov, Nikolai Nikolaevich}, title = {Deformation quantisation and boundary value problems}, volume = {4}, number = {5}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-77150}, pages = {27}, year = {2015}, abstract = {We describe a natural construction of deformation quantisation on a compact symplectic manifold with boundary. On the algebra of quantum observables a trace functional is defined which as usual annihilates the commutators. This gives rise to an index as the trace of the unity element. We formulate the index theorem as a conjecture and examine it by the classical harmonic oscillator.}, language = {en} } @unpublished{FladSchneiderSchulze2007, author = {Flad, Heinz-J{\"u}rgen and Schneider, Reinhold and Schulze, Bert-Wolfgang}, title = {Asymptotic regularity of solutions of Hartree-Fock equations with coulomb potential}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30268}, year = {2007}, abstract = {We study the asymptotic regularity of solutions of Hartree-Fock equations for Coulomb systems. In order to deal with singular Coulomb potentials, Fock operators are discussed within the calculus of pseudo-differential operators on conical manifolds. First, the non-self-consistent-field case is considered which means that the functions that enter into the nonlinear terms are not the eigenfunctions of the Fock operator itself. We introduce asymptotic regularity conditions on the functions that build up the Fock operator which guarantee ellipticity for the local part of the Fock operator on the open stretched cone R+ × S². This proves existence of a parametrix with a corresponding smoothing remainder from which it follows, via a bootstrap argument, that the eigenfunctions of the Fock operator again satisfy asymptotic regularity conditions. Using a fixed-point approach based on Cances and Le Bris analysis of the level-shifting algorithm, we show via another bootstrap argument, that the corresponding self-consistent-field solutions of the Hartree-Fock equation have the same type of asymptotic regularity.}, language = {en} } @unpublished{FlandoliHoegele2014, author = {Flandoli, Franco and H{\"o}gele, Michael}, title = {A solution selection problem with small stable perturbations}, volume = {3}, number = {8}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-71205}, pages = {43}, year = {2014}, abstract = {The zero-noise limit of differential equations with singular coefficients is investigated for the first time in the case when the noise is a general alpha-stable process. It is proved that extremal solutions are selected and the probability of selection is computed. Detailed analysis of the characteristic function of an exit time form on the half-line is performed, with a suitable decomposition in small and large jumps adapted to the singular drift.}, language = {en} } @unpublished{FradonRoelly2005, author = {Fradon, Myriam and Roelly, Sylvie}, title = {Infinite system of Brownian balls with interaction : the non-reversible case}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51546}, year = {2005}, abstract = {We consider an infinite system of hard balls in Rd undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite- dimensional Stochastic Differential Equation with an infinite-dimensional local time term. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also show that Gibbs measures are reversible measures.}, language = {en} } @unpublished{FradonRoelly2005, author = {Fradon, Myriam and Roelly, Sylvie}, title = {Infinite system of Brownian Balls: Equilibrium measures are canonical Gibbs}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51594}, year = {2005}, abstract = {We consider a system of infinitely many hard balls in Rd undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite-dimensional Stochastic Differential Equation with a local time term. We prove that the set of all equilibrium measures, solution of a Detailed Balance Equation, coincides with the set of canonical Gibbs measures associated to the hard core potential added to the smooth interaction potential.}, language = {en} } @unpublished{FradonRoelly2009, author = {Fradon, Myriam and Roelly, Sylvie}, title = {Infinitely many Brownian globules with Brownian radii}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49552}, year = {2009}, abstract = {We consider an infinite system of non overlaping globules undergoing Brownian motions in R3. The term globules means that the objects we are dealing with are spherical, but with a radius which is random and time-dependent. The dynamics is modelized by an infinitedimensional Stochastic Differential Equation with local time. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also find a class of reversible measures.}, language = {en} } @unpublished{FradonRoelly2005, author = {Fradon, Myriam and Roelly, Sylvie}, title = {Brownian Hard Balls submitted to an infinite rangeinteraction with slow decay}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49379}, year = {2005}, abstract = {We consider an infinite system of hard balls in Rd undergoing Brownian motions and submitted to a pair potential with infinite range and quasi polynomial decay. It is modelized by an infinite-dimensional Stochastic Differential Equation with an infinite-dimensional local time term. Existence and uniqueness of a strong solution is proven for such an equation with deterministic initial condition. We also show that the set of all equilibrium measures, solution of a Detailed Balance Equation, coincides with the set of canonical Gibbs measures associated to the hard core potential.}, language = {en} } @unpublished{GairingHoegeleKosenkova2016, author = {Gairing, Jan and H{\"o}gele, Michael and Kosenkova, Tetiana}, title = {Transportation distances and noise sensitivity of multiplicative L{\´e}vy SDE with applications}, volume = {5}, number = {2}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-86693}, pages = {24}, year = {2016}, abstract = {This article assesses the distance between the laws of stochastic differential equations with multiplicative L{\´e}vy noise on path space in terms of their characteristics. The notion of transportation distance on the set of L{\´e}vy kernels introduced by Kosenkova and Kulik yields a natural and statistically tractable upper bound on the noise sensitivity. This extends recent results for the additive case in terms of coupling distances to the multiplicative case. The strength of this notion is shown in a statistical implementation for simulations and the example of a benchmark time series in paleoclimate.}, language = {en} } @unpublished{GairingHoegeleKosenkovaetal.2013, author = {Gairing, Jan and H{\"o}gele, Michael and Kosenkova, Tetiana and Kulik, Alexei Michajlovič}, title = {Coupling distances between L{\´e}vy measures and applications to noise sensitivity of SDE}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-68886}, year = {2013}, abstract = {We introduce the notion of coupling distances on the space of L{\´e}vy measures in order to quantify rates of convergence towards a limiting L{\´e}vy jump diffusion in terms of its characteristic triplet, in particular in terms of the tail of the L{\´e}vy measure. The main result yields an estimate of the Wasserstein-Kantorovich-Rubinstein distance on path space between two L{\´e}vy diffusions in terms of the couping distances. We want to apply this to obtain precise rates of convergence for Markov chain approximations and a statistical goodness-of-fit test for low-dimensional conceptual climate models with paleoclimatic data.}, language = {en} } @unpublished{GairingHoegeleKosenkovaetal.2014, author = {Gairing, Jan and H{\"o}gele, Michael and Kosenkova, Tetiana and Kulik, Alexei Michajlovič}, title = {On the calibration of L{\´e}vy driven time series with coupling distances : an application in paleoclimate}, volume = {3}, number = {2}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-69781}, pages = {18}, year = {2014}, abstract = {This article aims at the statistical assessment of time series with large fluctuations in short time, which are assumed to stem from a continuous process perturbed by a L{\´e}vy process exhibiting a heavy tail behavior. We propose an easily implementable procedure to estimate efficiently the statistical difference between the noisy behavior of the data and a given reference jump measure in terms of so-called coupling distances. After a short introduction to L{\´e}vy processes and coupling distances we recall basic statistical approximation results and derive rates of convergence. In the sequel the procedure is elaborated in detail in an abstract setting and eventually applied in a case study to simulated and paleoclimate data. It indicates the dominant presence of a non-stable heavy-tailed jump L{\´e}vy component for some tail index greater than 2.}, language = {en} } @unpublished{Galstian2001, author = {Galstian, Anahit}, title = {Lp - Lq decay estimates for the equation with exponentially growing coefficient}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26079}, year = {2001}, abstract = {Contents: 1 Introduction 1 Representation formulas 2 Consideration in the pseudodifferential zone: e up(t) |ξ| ≤ 1 3 Consideration in he hyperbolic zone: e up(t) |ξ| ≥ 1}, language = {en} } @unpublished{GalstianYagdjian1997, author = {Galstian, Anahit and Yagdjian, Karen}, title = {Exponential function of pseudo-differential operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24982}, year = {1997}, abstract = {The paper is devoted to the construction of the exponential function of a matrix pseudo-differential operator which do not satisfy any of the known theorems (see, Sec.8 Ch.VIII and Sec.2 Ch.XI of [17]). The applications to the construction of the fundamental solution for the Cauchy problem for the hyperbolic operators with the characteristics of variable multiplicity are given, too.}, language = {en} } @unpublished{GauthierTarkhanov2004, author = {Gauthier, Paul M. and Tarkhanov, Nikolai Nikolaevich}, title = {A covering property of the Riemann zeta-function}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26683}, year = {2004}, abstract = {For each compact subset K of the complex plane C which does not surround zero, the Riemann surface Sζ of the Riemann zeta function restricted to the critical half-strip 0 < Rs < 1/2 contains infinitely many schlicht copies of K lying 'over' K. If Sζ also contains at least one such copy, for some K which surrounds zero, then the Riemann hypothesis fails.}, language = {en} } @unpublished{GibaliShoikhetTarkhanov2015, author = {Gibali, Aviv and Shoikhet, David and Tarkhanov, Nikolai Nikolaevich}, title = {On the convergence of continuous Newton method}, volume = {4}, number = {10}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-81537}, pages = {15}, year = {2015}, abstract = {In this paper we study the convergence of continuous Newton method for solving nonlinear equations with holomorphic mappings in complex Banach spaces. Our contribution is based on a recent progress in the geometric theory of spirallike functions. We prove convergence theorems and illustrate them by numerical simulations.}, language = {en} } @unpublished{GilKrainerMendoza2004, author = {Gil, Juan B. and Krainer, Thomas and Mendoza, Gerardo A.}, title = {Geometry and spectra of closed extensions of elliptic cone operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26815}, year = {2004}, abstract = {We study the geometry of the set of closed extensions of index 0 of an elliptic cone operator and its model operator in connection with the spectra of the extensions, and give a necessary and sufficient condition for the existence of rays of minimal growth for such operators.}, language = {en} } @unpublished{GilKrainerMendoza2004, author = {Gil, Juan B. and Krainer, Thomas and Mendoza, Gerardo A.}, title = {Resolvents of elliptic cone operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26820}, year = {2004}, abstract = {We prove the existence of sectors of minimal growth for general closed extensions of elliptic cone operators under natural ellipticity conditions. This is achieved by the construction of a suitable parametrix and reduction to the boundary. Special attention is devoted to the clarification of the analytic structure of the resolvent.}, language = {en} } @unpublished{GilKrainerMendoza2006, author = {Gil, Juan B. and Krainer, Thomas and Mendoza, Gerardo A.}, title = {On rays of minimal growth for elliptic cone operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30064}, year = {2006}, abstract = {We present an overview of some of our recent results on the existence of rays of minimal growth for elliptic cone operators and two new results concerning the necessity of certain conditions for the existence of such rays.}, language = {en} } @unpublished{Gilkey1998, author = {Gilkey, Peter}, title = {The heat content asymptotics for variable geometries}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25381}, year = {1998}, abstract = {We study the heat content asymptotics on a compact manifold with boundary defened by a time dependent family of operators of Laplace type.}, language = {en} } @unpublished{GlebovKiselev2005, author = {Glebov, S. G. and Kiselev, O. M.}, title = {The forced KdV equation and passage through resonance}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29975}, year = {2005}, abstract = {We construct a special asymptotic solution for the forced KdV equation. In the frame of the shallow water model this kind of the external driving force is related to the atmospheric disturbance. The perturbation slowly passes through a resonance and it leads to the solution exchange. The detailed asymptotic description of the process is presented.}, language = {en} }