TY  - INPR
A1  - Ly, Ibrahim
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Generalised Beltrami equations
N2  - We enlarge the class of Beltrami equations by developping a stability theory for the sheaf of solutions of an overdetermined elliptic system of first order homogeneous partial differential equations with constant coefficients in the Euclidean space.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)14 
KW  - Quasiconformal mapping
KW  - Beltrami equation
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-67416
ER  - 
TY  - INPR
A1  - Roelly, Sylvie
T1  - Reciprocal processes : a stochastic analysis approach
N2  - Reciprocal processes, whose concept can be traced back to E. Schrödinger, form a class of stochastic processes constructed as mixture of bridges, that satisfy a time Markov field property. We discuss here a new unifying approach to characterize several types of reciprocal processes via duality formulae on path spaces: The case of reciprocal processes with continuous paths associated to Brownian diffusions and the case of pure jump reciprocal processes associated to counting processes are treated. This presentation is based on joint works with M. Thieullen, R. Murr and C. Léonard.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 6 
KW  - Reciprocal process
KW  - Brownian bridge
KW  - Poisson bridge
KW  - duality formula
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-64588
SN  - 2193-6943
ER  - 
TY  - GEN
A1  - Dai Pra, Paolo
A1  - Louis, Pierre-Yves
A1  - Minelli, Ida
T1  - Monotonicity and complete monotonicity for continuous-time Markov chains
N2  - We analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions are not equivalent. However, we show that there are partially ordered sets for which monotonicity and complete monotonicity coincide in continuous time but not in discrete-time.
N2  - Nous étudions les notions de monotonie et de monotonie complète pour les processus de Markov (ou chaînes de Markov à temps continu) prenant leurs valeurs dans un espace partiellement ordonné. Ces deux notions ne sont pas équivalentes, comme c'est le cas lorsque le temps est discret. Cependant, nous établissons que pour certains ensembles partiellement ordonnés, l'équivalence a lieu en temps continu bien que n'étant pas vraie en temps discret.
KW  - Stochastik
KW  - continuous time Markov Chains
KW  - poset
KW  - monotonicity
KW  - coupling
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-7665
ER  - 
TY  - INPR
A1  - Savin, Anton
A1  - Sternin, Boris
T1  - Eta-invariant and Pontrjagin duality in K-theory
N2  - The topological significance of the spectral Atiyah-Patodi-Singer η-invariant is investigated. We show that twice the fractional part of the invariant is computed by the linking pairing in K-theory with the orientation bundle of the manifold. The Pontrjagin duality implies the nondegeneracy of the linking form. An example of a nontrivial fractional part for an even-order operator is presented.
T3  - Preprint - (2000) 08 
KW  - eta-invariant
KW  - K-theory
KW  - Pontrjagin duality
KW  - linking coefficients
KW  - Atiyah-Patodi-Singer theory
KW  - modulo n index
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25747
ER  - 
TY  - INPR
A1  - Airapetyan, Ruben
A1  - Witt, Ingo
T1  - Isometric properties of the Hankel Transformation in weighted sobolev spaces
N2  - It is shown that the Hankel transformation Hsub(v) acts in a class of weighted Sobolev spaces. Especially, the isometric mapping property of Hsub(v) which holds on L²(IRsub(+),rdr) is extended to spaces of arbitrary Sobolev order. The novelty in the approach consists in using techniques developed by B.-W. Schulze and others to treat the half-line Rsub(+) as a manifold with a conical singularity at r = 0. This is achieved by pointing out a connection between the Hankel transformation and the Mellin transformation.The procedure proposed leads at the same time to a short proof of the Hankel inversion formula. An application to the existence and higher regularity of solutions, including their asymptotics, to the 1-1-dimensional edge-degenerated wave equation is given.
T3  - Preprint - (1997) 14 
Y1  - 1997
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25001
ER  - 
TY  - INPR
A1  - Korkey, Michael Brian
T1  - Optimal factorization of Muckenhoupt weights
N2  - Peter Jones' theorem on the factorization of Ap weights is sharpened for weights with bounds near 1, allowing the factorization to be performed continuously near the limiting, unweighted case. When 1 < p < infinite and omega is an Ap weight with bound Ap(omega) = 1 + epsilon, it is shown that there exist Asub1 weights u, v such that both the formula omega = uv(1-p) and the estimates A1 (u), A1 (v) = 1 + Omikron (√epsilon) hold. The square root in these estimates is also proven to be the correct asymptotic power as epsilon -> 0.
T3  - Preprint - (1998) 15 
Y1  - 1998
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25266
ER  - 
TY  - INPR
A1  - Chen, Hua
A1  - Hidetoshi, Tahara
T1  - On the holomorphic solution of non-linear totally characteristic equations
N2  - 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 Gérard-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.
T3  - Preprint - (1998) 20 
KW  - Nonlinear
KW  - singular partial differential equation
KW  - holomorphic solution
Y1  - 1998
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25333
ER  - 
TY  - INPR
A1  - Lauter, Robert
A1  - Seiler, Jörg
T1  - Pseudodifferential analysis on manifolds with boundary - a comparison of b-calculus and cone algebra
N2  - We establish a relation between two different approaches to a complete pseudodifferential analysis of totally characteristic or Fuchs type operators on compact manifolds with boundary respectively conical singularities: Melrose's (overblown) b-calculus and Schulze's cone algebra. Though quite different in their definition, we show that these two pseudodifferential calculi basically contain the same operators.
T3  - Preprint - (1999) 27 
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25611
ER  - 
TY  - INPR
A1  - Kytmanov, Alexander
A1  - Myslivets, Simona
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Analytic representation of CR Functions on hypersurfaces with singularities
N2  - We prove a theorem on analytic representation of integrable CR functions on hypersurfaces with singular points. Moreover, the behaviour of representing analytic functions near singular points is investigated. We are aimed at explaining the new effect caused by the presence of a singularity rather than at treating the problem in full generality.
T3  - Preprint - (1999) 29 
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25631
ER  - 
TY  - INPR
A1  - Schrohe, Elmar
T1  - A short introduction to Boutet de Monvel's calculus
N2  - This paper provides an introduction to Boutet de Monvel's calculus on the half-space IRn (positiv) in the framework of a pseudodifferential calculus with operator-valued symbols.
T3  - Preprint - (2000) 03 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25696
ER  - 
TY  - INPR
A1  - Böckmann, Christine
A1  - Sarközi, Janos
T1  - The ill-posed inversion of multiwavelength lidar data by a hybrid method of variable projection
N2  - 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.
T3  - NLD Preprints - 53 
KW  - Ill-posed problem
KW  - inversion
KW  - variable projection method
KW  - multiwavelength Lidar
KW  - aerosol distribution
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14847
ER  - 
TY  - GEN
A1  - Ascher, Uri M.
A1  - Chin, Hongsheng
A1  - Reich, Sebastian
T1  - Stabilization of DAEs and invariant manifolds
N2  - Many methods have been proposed for the stabilization of higher index differential-algebraic equations (DAEs). Such methods often involve constraint differentiation and problem stabilization, thus obtaining a stabilized index reduction. A popular method is Baumgarte stabilization, but the choice of parameters to make it robust is unclear in practice. Here we explain why the Baumgarte method may run into trouble. We then show how to improve it. We further develop a unifying theory for stabilization methods which includes many of the various techniques proposed in the literature. Our approach is to (i) consider stabilization of ODEs with invariants, (ii) discretize the stabilizing term in a simple way, generally different from the ODE discretization, and (iii) use orthogonal projections whenever possible. The best methods thus obtained are related to methods of coordinate projection. We discuss them and make concrete algorithmic suggestions.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 030 
Y1  - 1994
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-15625
ER  - 
TY  - GEN
A1  - Reich, Sebastian
T1  - Smoothed dynamics of highly oscillatory Hamiltonian systems
N2  - We consider the numerical treatment of Hamiltonian systems that contain a potential which grows large when the system deviates from the equilibrium value of the potential. Such systems arise, e.g., in molecular dynamics simulations and the spatial discretization of Hamiltonian partial differential equations. Since the presence of highly oscillatory terms in the solutions forces any explicit integrator to use very small step size, the numerical integration of such systems provides a challenging task. It has been suggested before to replace the strong potential by a holonomic constraint that forces the solutions to stay at the equilibrium value of the potential. This approach has, e.g., been successfully applied to the bond stretching in molecular dynamics simulations. In other cases, such as the bond-angle bending, this methods fails due to the introduced rigidity. Here we give a careful analysis of the analytical problem by means of a smoothing operator. This will lead us to the notion of the smoothed dynamics of a highly oscillatory Hamiltonian system. Based on our analysis, we suggest a new constrained formulation that maintains the flexibility of the system while at the same time suppressing the high-frequency components in the solutions and thus allowing for larger time steps. The new constrained formulation is Hamiltonian and can be discretized by the well-known SHAKE method.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 031 
Y1  - 1995
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-15639
ER  - 
TY  - GEN
A1  - Leimkuhler, Benedict
A1  - Reich, Sebastian
T1  - Symplectic integration of constrained Hamiltonian systems
N2  - A Hamiltonian system in potential form (formula in the original abstract) subject to smooth constraints on q can be viewed as a Hamiltonian system on a manifold, but numerical computations must be performed in Rn. In this paper methods which reduce "Hamiltonian differential algebraic equations" to ODEs in Euclidean space are examined. The authors study the construction of canonical parameterizations or local charts as well as methods based on the construction of ODE systems in the space in which the constraint manifold is embedded which preserve the constraint manifold as an invariant manifold. In each case, a Hamiltonian system of ordinary differential equations is produced. The stability of the constraint invariants and the behavior of the original Hamiltonian along solutions are investigated both numerically and analytically.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 032 
KW  - differential-algebraic equations
KW  - constrained Hamiltonian systems
KW  - canonical discretization schemes
KW  - symplectic methods
Y1  - 1994
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-15653
ER  - 
TY  - GEN
A1  - Ascher, Uri M.
A1  - Chin, Hongsheng
A1  - Petzold, Linda R.
A1  - Reich, Sebastian
T1  - Stabilization of constrained mechanical systems with DAEs and invariant manifolds
N2  - Many methods have been proposed for the simulation of constrained mechanical systems. The most obvious of these have mild instabilities and drift problems. Consequently, stabilization techniques have been proposed A popular stabilization method is Baumgarte's technique, but the choice of parameters to make it robust has been unclear in practice. Some of the simulation methods that have been proposed and used in computations are reviewed here, from a stability point of view. This involves concepts of differential-algebraic equation (DAE) and ordinary differential equation (ODE) invariants. An explanation of the difficulties that may be encountered using Baumgarte's method is given, and a discussion of why a further quest for better parameter values for this method will always remain frustrating is presented. It is then shown how Baumgarte's method can be improved. An efficient stabilization technique is proposed, which may employ explicit ODE solvers in case of nonstiff or highly oscillatory problems and which relates to coordinate projection methods. Examples of a two-link planar robotic arm and a squeezing mechanism illustrate the effectiveness of this new stabilization method.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 033 
Y1  - 1994
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-15698
ER  - 
TY  - INPR
A1  - Shlapunov, Alexander
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Mixed problems with a parameter
N2  - Let X be a smooth n -dimensional manifold and D be an open connected set in X with smooth boundary ∂D. Perturbing the Cauchy problem for an elliptic system Au = f in D with data on a closed set Γ ⊂ ∂D we obtain a family of mixed problems depending on a small parameter ε > 0. Although the mixed problems are subject to a non-coercive boundary condition on ∂D\Γ in general, each of them is uniquely solvable in an appropriate Hilbert space DT and the corresponding family {uε} of solutions approximates the solution of the Cauchy problem in DT whenever the solution exists. We also prove that the existence of a solution to the Cauchy problem in DT is equivalent to the boundedness of the family {uε}. We thus derive a solvability condition for the Cauchy problem and an effective method of constructing its solution. Examples for Dirac operators in the Euclidean space Rn are considered. In the latter case we obtain a family of mixed boundary problems for the Helmholtz equation.
T3  - Preprint - (2004) 02 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26677
ER  - 
TY  - INPR
A1  - Berman, Gennady
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Quantum dynamics in the Fermi-Pasta-Ulam problem
N2  - 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.
T3  - Preprint - (2004) 05 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26695
ER  - 
TY  - INPR
A1  - Popivanov, Petăr R.
T1  - Lorenz transformations and creation of logarithmic singularities to the solutions of some nonstrictly hyperbolic semilinear systems with two space variables
T3  - Preprint - (2004) 07 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26710
ER  - 
TY  - INPR
A1  - Witt, Ingo
T1  - Green formulae for cone differential operators
N2  - Green formulae for elliptic cone differential operators are established. This is achieved by an accurate description of the maximal domain of an elliptic cone differential operator and its formal adjoint; thereby utilizing the concept of a discrete asymptotic type. From this description, the singular coefficients replacing the boundary traces in classical Green formulas are deduced.
T3  - Preprint - (2003) 20 
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26633
ER  - 
TY  - INPR
A1  - Kytmanov, Aleksandr
A1  - Myslivets, Simona
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Power sums of roots of a nonlinear system
N2  - For a system of meromorphic functions f = (f1, . . . , fn) in Cn, an explicit formula is given for evaluating negative power sums of the roots of the nonlinear system f(z) = 0.
T3  - Preprint - (2004) 18 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26788
ER  - 
TY  - INPR
A1  - Kytmanov, Aleksandr
A1  - Myslivets, Simona
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Zeta-function of a nonlinear system
N2  - Given a system of entire functions in Cn with at most countable set of common zeros, we introduce the concept of zeta-function associated with the system. Under reasonable assumptions on the system, the zeta-function is well defined for all s ∈ Zn with sufficiently large components. Using residue theory we get an integral representation for the zeta-function which allows us to construct an analytic extension of the zeta-function to an infinite cone in Cn.
T3  - Preprint - (2004) 19 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26795
ER  - 
TY  - INPR
A1  - Gil, Juan B.
A1  - Krainer, Thomas
A1  - Mendoza, Gerardo A.
T1  - Geometry and spectra of closed extensions of elliptic cone operators
N2  - 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.
T3  - Preprint - (2004) 21 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26815
ER  - 
TY  - INPR
A1  - Gil, Juan B.
A1  - Krainer, Thomas
A1  - Mendoza, Gerardo A.
T1  - Resolvents of elliptic cone operators
N2  - 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.
T3  - Preprint - (2004) 22 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26820
ER  - 
TY  - BOOK
A1  - Pilipenko, Andrey
T1  - An introduction to stochastic differential equations with reflection
T3  - Lectures in pure and applied mathematics
N2  - These lecture notes are intended as a short introduction to diffusion processes on a domain with a reflecting boundary for graduate students, researchers in stochastic analysis and interested readers. Specific results on stochastic differential equations with reflecting boundaries such as existence and uniqueness, continuity and Markov properties, relation to partial differential equations and submartingale problems are given. An extensive list of references to current literature is included. This book has its origins in a mini-course the author gave at the University of Potsdam and at the Technical University of Berlin in Winter 2013.
T3  - Lectures in pure and applied mathematics - 1 
KW  - Diffusionsprozess
KW  - Reflektierende Randbedingungen
KW  - stochastische Differentialgleichungen
KW  - diffusion process
KW  - reflecting boundary
KW  - stochastic differential equations
Y1  - 2014
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70782
SN  - 978-3-86956-297-1
SN  - 2199-4951
SN  - 2199-496X
IS  - 1
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Cattiaux, Patrick
A1  - Fradon, Myriam
A1  - Kulik, Alexei Michajlovič
A1  - Roelly, Sylvie
T1  - Long time behavior of stochastic hard ball systems
N2  - 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.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)15 
KW  - Stochastic differential equations
KW  - hard core interaction
KW  - reversible measure
KW  - normal reflection
KW  - local time
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-68388
ER  - 
TY  - GEN
A1  - Reich, Sebastian
T1  - Algebrodifferentialgleichungen und Vektorfelder auf Mannigfaltigkeiten
N2  - In diesem Beitrag wird der Zusammenhang zwischen Algebrodifferentialgleichungen (ADGL) und Vektorfeldern auf Mannigfaltigkeiten untersucht. Dazu wird zunächst der Begriff der regulären ADGL eingeführt, wobei unter eirter regulären ADGL eine ADGL verstanden wird, deren Lösungsmenge identisch mit der Lösungsmenge eines Vektorfeldes ist. Ausgehend von bekannten Aussagen über die Lösungsmenge eines Vektorfeldes werden analoge Aussagen für die Lösungsmenge einer regulären ADGL abgeleitet. Es wird eine Reduktionsmethode angegeben, die auf ein Kriterium für die Begularität einer ADGL und auf die Definition des Index einer nichtlinearen ADGL führt. Außerdem wird gezeigt, daß beliebige Vektorfelder durch reguläre ADGL so realisiert werden können, daß die Lösungsmenge des Vektorfeldes mit der der realisierenden ADGL identisch ist. Abschließend werden die für autonome ADGL gewonnenen Aussagen auf den Fall der nichtautonomen ADGL übertragen.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 160 
Y1  - 1980
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-47290
ER  - 
TY  - GEN
A1  - Reich, Sebastian
T1  - Differential-algebraic equations and applications in circuit theory
N2  - Technical and physical systems, especially electronic circuits, are frequently modeled as a system of differential and nonlinear implicit equations. In the literature such systems of equations are called differentialalgebraic equations (DAEs). It turns out that the numerical and analytical properties of a DAE depend on an integer called the index of the problem. For example, the well-known BDF method of Gear can be applied, in general, to a DAE only if the index does not exceed one. In this paper we give a geometric interpretation of higherindex DAEs and indicate problems arising in connection with such DAEs by means of several examples.
N2  - Die mathematische Modellierung technisch physikalischer Systeme wie elektrische Netzwerke, führt häufig auf ein System von Differentialgleichungen und nichtlinearen impliziten Gleichungen sogenannten Algebrodifferentialgleichungen (ADGL). Es zeigt sich, daß die numerischen und analytischen Eigenschaften von ADGL durch den Index des Problems charakterisiert werden können. Insbesondere können die bekannten Integrationsformeln von Gear im allgemeinen nur auf ADGL mit dem Index eins angewendet werden. In diesem Beitrag wird eine geometrische Interpretation von ADGL mit einem höheren Index gegeben sowie auf Probleme im Zusammenhang mit derartigen ADGL an Hand verschiedener Beispiele hingewiesen.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 156 
Y1  - 1992
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-46646
ER  - 
TY  - THES
A1  - Hohberger, Horst
T1  - Semiclassical asymptotics for the scattering amplitude in the presence of focal points at infinity
T1  - Semiklassische Asymptotik der Streuamplitude bei unendlich fernen Fokalpunkten
N2  - We consider scattering in $\R^n$, $n\ge 2$, described by the Schr\"odinger operator $P(h)=-h^2\Delta+V$, where $V$ is a short-range potential. With the aid of Maslov theory, we give a geometrical formula for the semiclassical asymptotics as $h\to 0$ of the scattering amplitude $f(\omega_-,\omega_+;\lambda,h)$ $\omega_+\neq\omega_-$) which remains valid in the presence of focal points at infinity (caustics). Crucial for this analysis are precise estimates on the asymptotics of the classical phase trajectories and the relationship between caustics in euclidean phase space and caustics at infinity.
N2  - Wir betrachten Streuung in $\R^n$, $n\ge 2$, beschrieben durch den Schr\"odinger operator $P(h)=-h^2\Delta+V$, wo $V$ ein kurzreichweitiges Potential ist. Mit Hilfe von Maslov Theorie erhalten wir eine geometrische Formel fuer die semiklassische Asymptotik ($h\to 0$) der Streuamplitude $f(\omega_-,\omega_+;\lambda,h)$ ($\omega_+\neq\omega_-$) welche auch bei Vorhandensein von Fokalpunkten bei Unendlich (Kaustiken) gueltig bleibt.
KW  - Mathematik
KW  - Physik
KW  - Streutheorie
KW  - Streuamplitude
KW  - Semiklassik
KW  - mathematics
KW  - physics
KW  - scattering theory
KW  - semiclassics
KW  - scattering amplitude
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-11574
ER  - 
TY  - GEN
A1  - Ginoux, Nicolas
T1  - Dirac operators on Lagrangian submanifolds
N2  - We study a natural Dirac operator on a Lagrangian submanifold of a Kähler manifold. We first show that its square coincides with the Hodge - de Rham Laplacian provided the complex structure identifies the Spin structures of the tangent and normal bundles of the submanifold. We then give extrinsic estimates for the eigenvalues of that operator and discuss some examples.
KW  - Dirac operators
KW  - Global Analysis
KW  - Spectral Geometry
KW  - Spin Geometry
KW  - Lagrangian submanifolds
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-5627
ER  - 
TY  - GEN
A1  - Ginoux, Nicolas
T1  - Remarques sur le spectre de l'opérateur de Dirac
T1  - Remarks on the spectrum of the Dirac operator
N2  - Nous décrivons un nouvelle famille d'exemples d'hypersurfaces de la sphère satisfaisant le cas d'égalité de la majoration extrinsèque de C. Bär de la plus petite valeur propre de l'opérateur de Dirac.
N2  - We describe a new family of examples of hypersurfaces in the sphere satisfying the limitingcase in C. Bär's extrinsic upper bound for the smallest eigenvalue of the Dirac operator.
KW  - 1st Eigenvalue
KW  - Submanifolds
KW  - Bounds
KW  - Space
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-5630
ER  - 
TY  - GEN
A1  - Louis, Pierre-Yves
T1  - Ergodicity of PCA
BT  - equivalence between spatial and temporal mixing conditions
N2  - For a general attractive Probabilistic Cellular Automata on S-Zd, we prove that the (time-) convergence towards equilibrium of this Markovian parallel dynamics, exponentially fast in the uniform norm, is equivalent to a condition (A). This condition means the exponential decay of the influence from the boundary for the invariant measures of the system restricted to finite boxes. For a class of reversible PCA dynamics on {1,+1}(Zd), wit a naturally associated Gibbsian potential rho, we prove that a (spatial-) weak mixing condition (WM) for rho implies the validity of the assumption (A); thus exponential (time-) ergodicity of these dynamics towards the unique Gibbs measure associated to rho hods. On some particular examples we state that exponential ergodicity holds as soon as there is no phase transition.
KW  - Wahrscheinlichkeitstheorie
KW  - Wechselwirkende Teilchensysteme
KW  - Stochastische Zellulare Automaten
KW  - Interacting particle systems
KW  - Probabilistic Cellular Automata
KW  - ERgodicity of Markov Chains
KW  - Gibbs measures
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6589
ER  - 
TY  - JOUR
A1  - Zagrebnov, Valentin
T1  - Trotter product formula on Hilbert and Banach spaces for operator-norm convergence
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-471971
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
SP  - 23
EP  - 34
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Sukiasyan, Hayk
A1  - Melkonyan, Tatev
T1  - Semi-recursive algorithm of piecewise linear approximation of two-dimensional function by the method of worst segment dividing
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-471982
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 35
EP  - 44
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Boldrighini, Carlo
A1  - Frigio, Sandro
A1  - Maponi, Pierluigi
A1  - Pellegrinotti, Alessandro
A1  - Sinai, Yakov G.
T1  - 3-D incompressible Navier-Stokes equations: Complex blow-up and related real flows
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472201
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 185
EP  - 194
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Figari, Rodolfo
A1  - Teta, Alessandro
T1  - Zero-range hamiltonians for three quantum particles
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472189
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 175
EP  - 184
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Jansen, Sabine
A1  - Kuna, Tobias
A1  - Tsagkarogiannis, Dimitrios
T1  - Virial inversion for inhomogeneous systems
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472111
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 135
EP  - 144
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Hryniv, Ostap
A1  - Wallace, Clare
T1  - Phase separation and sharp large deviations
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472168
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 155
EP  - 164
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Jansen, Sabine
A1  - Kolesnikov, Leonid
T1  - Activity expansions for Gibbs correlation functions
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472121
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 145
EP  - 154
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Jansen, Sabine
A1  - Tsagkarogiannis, Dimitrios
T1  - Mayer expansion for the Asakura-Oosawa model of colloid theory
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472109
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 127
EP  - 134
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Piatnitski, Andrey
A1  - Zhizhina, Elena
T1  - Non-local convolution type parabolic equations with fractional and regular time derivative
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472024
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 65
EP  - 67
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Jursenas, Rytis
T1  - The peak model for finite rank supersingular perturbations
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472090
IS  - 6
SP  - 117
EP  - 126
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Pechersky, Eugeny
A1  - Pirogov, Sergei
A1  - Yambartsev, Anatoly
T1  - Large emissions
BT  - Hawking-Penrose black hole model
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472049
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 77
EP  - 86
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Poghosyan, Suren
A1  - Zessin, Hans
T1  - Construction of limiting Gibbs processes and the uniqueness of Gibbs processes
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472015
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 55
EP  - 64
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Lykov, Alexander
A1  - Malyshev, Vadim
T1  - When bounded chaos becomes unbounded
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472060
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 97
EP  - 106
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Khachatryan, Linda
A1  - Nahapetian, Boris
T1  - On direct and inverse problems in the description of lattice random fields
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472083
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 107
EP  - 116
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Rafler, Mathias
T1  - Pinned Gibbs processes
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472007
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 45
EP  - 53
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Savin, Anton
A1  - Sternin, Boris
T1  - Eta invariant and parity conditions
N2  - We give a formula for the η-invariant of odd order operators on even-dimensional manifolds, and for even order operators on odd-dimensional manifolds. Geometric second order operators are found with nontrivial η-invariants. This solves a problem posed by P. Gilkey.
T3  - Preprint - (2000) 21 
KW  - eta invariant
KW  - parity conditions
KW  - K-theory
KW  - linking coefficients
KW  - Dirac operators
KW  - spectral flow
KW  - elliptic operators
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25869
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Sternin, Boris
T1  - On surgery in elliptic theory
N2  - We prove a general theorem on the behavior of the relative index under surgery for a wide class of Fredholm operators, including relative index theorems for elliptic operators due to Gromov-Lawson, Anghel, Teleman, Booß-Bavnbek-Wojciechowski, et al. as special cases. In conjunction with additional conditions (like symmetry conditions), this theorem permits one to compute the analytical index of a given operator. In particular, we obtain new index formulas for elliptic pseudodifferential operators and quantized canonical transformations on manifolds with conical singularities.
T3  - Preprint - (2000) 22 
KW  - elliptic operators
KW  - index theory
KW  - surgery
KW  - relative index
KW  - manifold with singularities
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25873
ER  - 
TY  - INPR
A1  - Coriasco, Sandro
A1  - Panarese, Paolo
T1  - Fourier integral operators defined by classical symbols with exit behaviour
N2  - 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].
T3  - Preprint - (2000) 24 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25896
ER  - 
TY  - INPR
A1  - Kytmanov, Aleksandr
A1  - Myslivets, Simona
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Removable singularities of CR functions on singular boundaries
N2  - The problem of analytic representation of integrable CR functions on hypersurfaces with singularities is treated. The nature o singularities does not matter while the set of singularities has surface measure zero. For simple singularities like cuspidal points, edges, corners, etc., also the behaviour of representing analytic functions near singular points is studied.
T3  - Preprint - (2000) 18 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25836
ER  - 
TY  - INPR
A1  - Tepoyan, Liparit
T1  - Degenerated operator equations of higher order
N2  - Content: 1 Introduction 2 The one-dimensional case 2.1 The space Wm sub (α) 2.2 Self-adjoint Equation 2.3 Non-selfadjoint Equation 3 Operator Equation
T3  - Preprint - (2000) 23 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25888
ER  - 
TY  - INPR
A1  - Krainer, Thomas
T1  - The calculus of Volterra Mellin pseudodifferential operators with operator-valued symbols
N2  - We introduce the calculus of Mellin pseudodifferential operators parameters based on "twisted" operator-valued Volterra symbols as well aas the abstract Mellin calclus with holomorphic symbols. We establish the properties of the symblic and operational calculi, and we give and make use of explicit oscillatory integral formulas on the symbolic side, e. g., for the Leibniz-product, kernel cut-off, and Mellin quantization. Moreover, we introduce the notion of parabolicity for the calculi of Volterra Mellin operators, and construct Volterra parametrices for parabolic operators within the calculi.
T3  - Preprint - (2001) 35 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26185
ER  - 
TY  - INPR
A1  - Xiaochun, Liu
A1  - Witt, Ingo
T1  - Pseudodifferential calculi on the half-line respecting prescribed asymptotic types
N2  - Contents: 1. Introduction 2. Preliminaries 3. Basic Elements of the Calculus 4. Further Elements of the Calculus
T3  - Preprint - (2002) 06 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26255
ER  - 
TY  - INPR
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Anisotropic edge problems
N2  - We investigate elliptic pseudodifferential operators which degenerate in an anisotropic way on a submanifold of arbitrary codimension. To find Fredholm problems for such operators we adjoint to them boundary and coboundary conditions on the submanifold.The algebra obtained this way is a far reaching generalisation of Boutet de Monvel's algebra of boundary value problems with transmission property. We construct left and right regularisers and prove theorems on hypoellipticity and local solvability.
T3  - Preprint - (2002) 09 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26280
ER  - 
TY  - INPR
A1  - Witt, Ingo
T1  - A calculus for a class of finitely degenerate pseudodifferential operators
N2  - For a class of degenerate pseudodifferential operators, local parametrices are constructed. This is done in the framework of a pseudodifferential calculus upon adding conditions of trace and potential type, respectively, along the boundary on which the operators degenerate.
T3  - Preprint - (2002) 05 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26246
ER  - 
TY  - INPR
A1  - Liu, Weian
A1  - Yang, Yin
A1  - Lu, Gang
T1  - Viscosity solutions of fully nonlinear parabolic systems
N2  - In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in [2] and [3].
T3  - Preprint - (2002) 02 
KW  - Viscosity solutions
KW  - systems of partial differential equations
KW  - fully non-linear degenerate parabolic equations
KW  - Perron's method
KW  - coupled solution
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26215
ER  - 
TY  - INPR
A1  - Schrohe, Elmar
A1  - Seiler, Jörg
T1  - Ellipticity and invertibility in the cone algebra on Lp-Sobolev spaces
N2  - Given a manifold B with conical singularities, we consider the cone algebra with discrete asymptotics, introduced by Schulze, on a suitable scale of Lp-Sobolev spaces. Ellipticity is proven to be equivalent to the Fredholm property in these spaces, it turns out to be independent of the choice of p. We then show that the cone algebra is closed under inversion: whenever an operator is invertible between the associated Sobolev spaces, its inverse belongs to the calculus. We use these results to analyze the behaviour of these operators on Lp(B).
T3  - Preprint - (1999) 28 
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25621
ER  - 
TY  - INPR
A1  - Fedosov, Boris
T1  - Pseudo-differential operators and deformation quantization
N2  - 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.
T3  - Preprint - (1999) 32 
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25651
ER  - 
TY  - INPR
A1  - Sadykov, Timour
T1  - Hypergeometric systems of differential equations and amoebas of rational functions
N2  - We study the approach to the theory of hypergeometric functions in several variables via a generalization of the Horn system of differential equations. A formula for the dimension of its solution space is given. Using this formula we construct an explicit basis in the space of holomorphic solutions to the generalized Horn system under some assumptions on its parameters. These results are applied to the problem of describing the complement of the amoeba of a rational function, which was posed in [12].
T3  - Preprint - (1999) 33 
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25665
ER  - 
TY  - INPR
A1  - Shlapunov, Alexander
T1  - On Iterations of double layer potentials
N2  - We prove the existence of Hp(D)-limit of iterations of double layer potentials constructed with the use of Hodge parametrix on a smooth compact manifold X, D being an open connected subset of X. This limit gives us an orthogonal projection from Sobolev space Hp(D) to a closed subspace of Hp(D)-solutions of an elliptic operator P of order p ≥ 1. Using this result we obtain formulae for Sobolev solutions to the equation Pu = f in D whenever these solutions exist. This representation involves the sum of a series whose terms are iterations of double layer potentials. Similar regularization is constructed also for a P-Neumann problem in D.
T3  - Preprint - (2000) 02 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25687
ER  - 
TY  - INPR
A1  - Myslivets, Simona
T1  - On the boundary behaviour of the logarithmic residue integral
N2  - A formula of multidimensional logarithmic residue is proved for holomorphic maps with zeroes on the boundary of a bounded domain in Cn.
T3  - Preprint - (2000) 07 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25733
ER  - 
TY  - INPR
A1  - Coriasco, Sandro
A1  - Schrohe, Elmar
A1  - Seiler, Jörg
T1  - Bounded imaginary powers of differential operators on manifolds with conical singularities
N2  - 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.
T3  - Preprint - (2001) 12 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25962
ER  - 
TY  - INPR
A1  - Xiaochun, Liu
A1  - Witt, Ingo
T1  - Asymptotic expansions for bounded solutions to semilinear Fuchsian equations
N2  - It is shown that bounded solutions to semilinear elliptic Fuchsian equations obey complete asymptoic expansions in terms of powers and logarithms in the distance to the boundary. For that purpose, Schuze's notion of asymptotic type for conormal asymptotics close to a conical point is refined. This in turn allows to perform explicit calculations on asymptotic types - modulo the resolution of the spectral problem for determining the singular exponents in the asmptotic expansions.
T3  - Preprint - (2001) 01 
KW  - Calculus of conormal symbols
KW  - conormal asymptotic expansions
KW  - discrete saymptotic types
KW  - weighted Sobolev spaces with discrete saymptotics
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25912
ER  - 
TY  - INPR
A1  - Ma, Li
A1  - Xu, Xingwang
T1  - Positive solutions of a logistic equation on unbounded intervals
N2  - In this paper, we study the existence of positive solutions of a one-parameter family of logistic equations on R+ or on R. These equations are stationary versions of the Fisher equations and the KPP equations. We also study the blow up region of a sequence of the solutions when the parameter approachs a critical value and the nonexistence of positive solutions beyond the critical value. We use the direct method and the sub and super solution method.
T3  - Preprint - (2001) 17 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26015
ER  - 
TY  - INPR
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Harmonic integrals on domains with edges
N2  - We study the Neumann problem for the de Rham complex in a bounded domain of Rn with singularities on the boundary. The singularities may be general enough, varying from Lipschitz domains to domains with cuspidal edges on the boundary. Following Lopatinskii we reduce the Neumann problem to a singular integral equation of the boundary. The Fredholm solvability of this equation is then equivalent to the Fredholm property of the Neumann problem in suitable function spaces. The boundary integral equation is explicitly written and may be treated in diverse methods. This way we obtain, in particular, asymptotic expansions of harmonic forms near singularities of the boundary.
T3  - Preprint - (2004) 20 
KW  - domains with singularities
KW  - de Rham complex
KW  - Neumann problem
KW  - Hodge theory
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26800
ER  - 
TY  - INPR
A1  - Krainer, Thomas
T1  - On the inverse of parabolic boundary value problems for large times
N2  - We construct algebras of Volterra pseudodifferential operators that contain, in particular, the inverses of the most natural classical systems of parabolic boundary value problems of general form. Parabolicity is determined by the invertibility of the principal symbols, and as a result is equivalent to the invertibility of the operators within the calculus. Existence, uniqueness, regularity, and asymptotics of solutions as t → ∞ are consquences of the mapping properties of the operators in exponentially weighted Sobolev spaces and subspaces with asymptotics. An important aspect of this work is that the microlocal and global kernel structure of the inverse operator (solution operator) of a parabolic boundary value problem for large times is clarified. Moreover, our approach naturally yields qualitative pertubation results for the solvability theory of parabolic boundary value problems. To achieve these results, we assign t = ∞ the meaning of a conical point and treat the operators as totally characteristic pseudodifferential boundary value problems.
T3  - Preprint - (2002) 12 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26310
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Sternin, Boris
T1  - Relative elliptic theory
N2  - This paper is a survey of relative elliptic theory (i.e. elliptic theory in the category of smooth embeddings), closely related to the Sobolev problem, first studied by Sternin in the 1960s. We consider both analytic aspects to the theory (the structure of the algebra of morphismus, ellipticity, Fredholm property) and topological aspects (index formulas and Riemann-Roch theorems). We also study the algebra of Green operators arising as a subalgebra of the algebra of morphisms.
T3  - Preprint - (2002) 23 
KW  - Sobolev problem
KW  - elliptic morphism
KW  - (co)boundary operator
KW  - Green operator
KW  - index
KW  - Riemann-Roch theorem
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26400
ER  - 
TY  - INPR
A1  - Davis, Simon
T1  - On the absence of large-order divergences in superstring theory
N2  - 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.
T3  - Preprint - (2002) 28 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26452
ER  - 
TY  - INPR
A1  - Junker, Wolfgang
A1  - Schrohe, Elmar
T1  - Adiabatic vacuum states on general spacetime manifolds : definition, construction, and physical properties
N2  - Adiabatic vacuum states are a well-known class of physical states for linear quantum fields n Robertson-Walker spacetimes. We extend the definition of adiabatic vacua to general spacetime manifolds by using the notion of the Sobolev wavefront set. This definition is also applicable to interacting field theories. Hadamard states form a special subclass of the adiabatic vacua. We analyze physical properties of adiabatic vacuum representations of the Klein-Gordon field on globally hyperbolic spacetme manifolds (factoriality, quasiequivalence, local definteness, Haag duality) and construct them explicitly, if the manifold has a compact Cauchy surface.
T3  - Preprint - (2001) 27 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26100
ER  - 
TY  - INPR
A1  - Yagdjian, Karen
T1  - Geometric optics for the nonlinear hyperbolic systems of Kirchhoff-type
N2  - Contents: 1 Introduction 2 Main result 3 Construction of the asymptotic solutions 3.1 Derivation of the equations for the profiles 3.2 Exsistence of the principal profile 3.3 Determination of Usub(2) and the remaining profiles 4 Stability of the samll global solutions. Justification of One Phase Nonlinear Geometric Optics for the Kirchhoff-type equations 4.1 Stability of the global solutions to the Kirchhoff-type symmetric hyperbolic systems 4.2 The nonlinear system of ordinary differential equations with the parameter 4.3 Some energies estimates 4.4 The dependence of the solution W(t, ξ) on the function s(t) 4.5 The oscillatory integrals of the bilinear forms of the solutions 4.6 Estimates for the basic bilinear form Γsub(s)(t) 4.7 Contraction mapping 4.8 Stability of the global solution 4.9 Justification of One Phase Nonlinear Geometric Optics for the Kirchhoff-type equations
T3  - Preprint - (2001) 22 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26059
ER  - 
TY  - INPR
A1  - Yihong, Du
A1  - Li, Ma
T1  - Some remarks related to De Giorgi's conjecture
N2  - For several classes of functions including the special case f(u) = u − u³, we obtain boundedness and symmetry results for solutions of the problem −Δu = f(u) defined on R up(n). Our results complement a number of recent results related to a conjecture of De Giorgi.
T3  - Preprint - (2001) 18 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26027
ER  - 
TY  - INPR
A1  - Galstian, Anahit
T1  - Lp - Lq decay estimates for the equation with exponentially growing coefficient
N2  - 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
T3  - Preprint - (2001) 24 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26079
ER  - 
TY  - INPR
A1  - Harutyunyan, Anahit V.
T1  - Toeplitz operators and division theorems in anisotropic spaces of holomorphic functions in the polydisc
N2  - This work is an introduction to anisotropic spaces, which have an ω-weight of analytic functions and are generalizations of Lipshitz classes in the polydisc. We prove that these classes form an algebra and are invariant with respect to monomial multiplication. These operators are bounded in these (Lipshitz and Djrbashian) spaces. As an application, we show a theorem about the division by good-inner functions in the mentioned classes is proved.
T3  - Preprint - (2001) 28 
KW  - Toeplitz operators
KW  - anisotropic spaces
KW  - polydisc
KW  - good-inner function
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26110
ER  - 
TY  - INPR
A1  - Maniccia, L.
A1  - Mughetti, M.
T1  - Weyl calculus for a class of subelliptic operators
N2  - Weyl-Hörmander calculus is used to get a parametrix in OPS¹-m sub(½, ½)(Ω)for a class of subelliptic pseudodifferential operators in OPS up(m)sub(1, 0)(Ω) with real non-negative principal symbol.
T3  - Preprint - (2001) 19 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26038
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Sternin, Boris
T1  - Some problems of control of semiclassical states for the Schrödinger equation
N2  - Contents: Introduction Controlled Quantum Systems The Asymptotic Controllability Problem The Stabilization Problem Unitarily Nonlinear Equations The Quantum Problem The Stabilization Problem for the Schrödinger Equation with a Unitarily Non-linear Control
T3  - Preprint - (2001) 30 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26130
ER  - 
TY  - INPR
A1  - Witt, Ingo
T1  - Asymptotic algebras
N2  - The concept of asymptotic type that primarily appears in singular and asymptotic analysis is developed. Especially, asymptotic algebras are introduced.
T3  - Preprint - (2001) 23 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26069
ER  - 
TY  - INPR
A1  - Rozenblum, G.
T1  - On some analytical index formulas related to operator-valued symbols
N2  - For several classes of pseudodifferential operators with operator-valued symbol analytic index formulas are found. The common feature is that uasual index formulas are not valid for these operators. Applications are given to pseudodifferential operators on singular manifolds.
T3  - Preprint - (2000) 16 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25811
ER  - 
TY  - INPR
A1  - Schrohe, Elmar
A1  - Seiler, Jörg
T1  - The resolvent of closed extensions of cone differential operators
N2  - We study an elliptic differential operator on a manifold with conical singularities, acting as an unbounded operator on a weighted Lp-space. Under suitable conditions we show that the resolvent (λ - A )-¹ exists in a sector of the complex plane and decays like 1/|λ| as |λ| -> ∞. Moreover, we determine the structure of the resolvent with enough precision to guarantee existence and boundedness of imaginary powers of A. As an application we treat the Laplace-Beltrami operator for a metric with striaght conical degeneracy and establish maximal regularity for the Cauchy problem u - Δu = f, u(0) = 0.
T3  - Preprint - (2002) 19 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26378
ER  - 
TY  - INPR
A1  - Calin, Ovidium
A1  - Der-Chen, Chang
T1  - The geometry on a step 3 Grushin model
N2  - 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.
T3  - Preprint - (2004) 08 
KW  - Grushin operator
KW  - subRiemannian geometry
KW  - geodesics
KW  - Hamilton-Jacobi theory
KW  - elliptic functions
KW  - Euler's theta functions
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26724
ER  - 
TY  - INPR
A1  - Gauthier, Paul M.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A covering property of the Riemann zeta-function
N2  - 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.
T3  - Preprint - (2004) 03 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26683
ER  - 
TY  - INPR
A1  - Kytmanov, Alexander
A1  - Myslivets, Simona
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Holomorphic Lefschetz formula for manifolds with boundary
N2  - The classical Lefschetz fixed point formula expresses the number of fixed points of a continuous map f : M -> M in terms of the transformation induced by f on the cohomology of M. In 1966 Atiyah and Bott extended this formula to elliptic complexes over a compact closed manifold. In particular, they presented a holomorphic Lefschtz formula for compact complex manifolds without boundary, a result, in the framework of algebraic geometry due to Eichler (1957) for holomorphic curves. On compact complex manifolds with boundary the Dolbeault complex is not elliptic, hence the Atiyah-Bott theory is no longer applicable. To get rid of the difficulties related to the boundary behaviour of the Dolbeault cohomology, Donelli and Fefferman (1986) derived a fixed point formula for the Bergman metric. The purpose of this paper is to present a holomorphic Lefschtz formula on a compact complex manifold with boundary
T3  - Preprint - (2002) 17 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26354
ER  - 
TY  - INPR
A1  - De-Xing, Kong
A1  - Hui, Yao
T1  - Global exact boundary controllability of a class of quasilinear hyperbolic systems of conservation laws II
N2  - 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.
T3  - Preprint - (2003) 08 
KW  - Quasilinear hyperbolic system
KW  - conservation laws
KW  - global exact boundary controllability
KW  - Cauchy problem
KW  - Goursat problem
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26565
ER  - 
TY  - INPR
A1  - Huicheng, Yin
A1  - Witt, Ingo
T1  - Global singularity structure of weak solutions to 3-D semilinear dispersive wave equations with discontinuous initial data
T3  - Preprint - (2002) 21 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26395
ER  - 
TY  - INPR
A1  - Camalès, Renaud
T1  - A note on the ramified Cauchy problem
N2  - 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.
T3  - Preprint - (2003) 21 
KW  - Ramified Cauchy problem
KW  - analytic continuation
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26646
ER  - 
TY  - INPR
A1  - Shlapunov, Alexander
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Duality by reproducing kernels
N2  - Let A be a determined or overdetermined elliptic differential operator on a smooth compact manifold X. Write Ssub(A)(D) for the space of solutions to thesystem Au = 0 in a domain D ⊂ X. Using reproducing kernels related to various Hilbert structures on subspaces of Ssub(A)(D) we show explicit identifications of the dual spaces. To prove the "regularity" of reproducing kernels up to the boundary of D we specify them as resolution operators of abstract Neumann problems. The matter thus reduces to a regularity theorem for the Neumann problem, a well-known example being the ∂-Neumann problem. The duality itself takes place only for those domains D which possess certain convexity properties with respect to A.
T3  - Preprint - (2001) 26 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26095
ER  - 
TY  - GEN
A1  - Reich, Sebastian
T1  - On a geometrical interpretation of differential-algebraic equations
N2  - The subject of this paper is the relation of differential-algebraic equations (DAEs) to vector fields on manifolds. For that reason, we introduce the notion of a regular DAE as a DAE to which a vector field uniquely corresponds. Furthermore, a technique is described which yields a family of manifolds for a given DAE. This socalled family of constraint manifolds allows in turn the formulation of sufficient conditions for the regularity of a DAE. and the definition of the index of a regular DAE. We also state a method for the reduction of higher-index DAEs to lowsr-index ones that can be solved without introducing additional constants of integration. Finally, the notion of realizability of a given vector field by a regular DAE is introduced, and it is shown that any vector field can be realized by a regular DAE. Throughout this paper the problem of path-tracing is discussed as an illustration of the mathematical phenomena.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 157 
Y1  - 1990
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-46683
ER  - 
TY  - GEN
A1  - Champagnat, Nicolas
A1  - Roelly, Sylvie
T1  - Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions
N2  - A multitype Dawson-Watanabe process is conditioned, in subcritical and critical cases, on non-extinction in the remote future. On every finite time interval, its distribution is absolutely continuous with respect to the law of the unconditioned process. A martingale problem characterization is also given. Several results on the long time behavior of the conditioned mass process - the conditioned multitype Feller branching diffusion - are then proved. The general case is first considered, where the mutation matrix which models the interaction between the types, is irreducible. Several two-type models with decomposable mutation matrices are analyzed too .
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 065 
KW  - multitype measure-valued branching processes
KW  - conditioned
KW  - critical and subcritical Dawson-Watanabe process
KW  - conditioned Feller diffusion
Y1  - 2008
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-18610
ER  - 
TY  - GEN
A1  - Reich, Sebastian
T1  - Momentum conserving symplectic integrators
N2  - In this paper, we show that symplectic partitioned Runge-Kutta methods conserve momentum maps corresponding to linear symmetry groups acting on the phase space of Hamiltonian differential equations by extended point transformation. We also generalize this result to constrained systems and show how this conservation property relates to the symplectic integration of Lie-Poisson systems on certain submanifolds of the general matrix group GL(n).
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 044 
Y1  - 1994
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-16824
ER  - 
TY  - GEN
A1  - Imkeller, Peter
A1  - Roelly, Sylvie
T1  - Die Wiederentdeckung eines Mathematikers: Wolfgang Döblin
N2  - "Considerons une particule mobile se mouvant aleatoirement sur la droite (ou sur un segment de droite). Supposons qu'il existe une probabilite F(x,y;s,t) bien definie pour que la particule se trouvant a l'instant s dans la position x se trouve a l'instant t (> s) a gauche de y, probabilite independante du mouvement anterieur de la particule...." Mit diesen Worten beginnt eines der berühmtesten mathematischen Manuskripte des letzten Jahrhunderts. Es stammt vom Soldaten Wolfgang Döblin, Sohn des deutschen Schriftstellers Alfred Döblin, und trägt den Titel "Sur l'equation de Kolmogoroff". Seine Veröffentlichung verbindet sich mit einer unglaublichen Geschichte. Wolfgang Döblin, stationiert mit seiner Einheit in den Ardennen im Winter 1939/1940, arbeitete an diesem Manuskript. Er entschloss sich, es als versiegeltes Manuskript an die Academie des Sciences in Paris zu schicken. Aber er kehrte nie aus diesem Krieg zurück. Sein Manuskript blieb 60 Jahre unter Verschluss im Archiv, und wurde erst im Jahre 2000 geöffnet. Wie weit Döblin damit seiner Zeit voraus war, wurde erkannt, nachdem es von Bernard Bru und Marc Yor ausgewertet worden war. Im ersten Satz umschreibt W. Döblin gleichzeitig das Programm des Manuskripts: "Wir betrachten ein bewegliches Teilchen, das sich zufällig auf der Geraden (oder einem Teil davon) bewegt." Er widmet sich damit der Aufgabe, die Fundamente eines Gebiets zu legen, das wir heute als stochastische Analysis bezeichnen.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 035 
KW  - Kolmogorov-Gleichung
KW  - Stochastische Analysis
KW  - Döblin
KW  - Wolfgang
KW  - Doblin
KW  - Vincent
KW  - Doeblin
KW  - Wolfgang
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-16397
ER  - 
TY  - INPR
A1  - Siegert, Sabine
T1  - Das Sankt-Petersburg-Paradoxon
N2  - Aus dem Inhalt: 1 Einleitung 2 Historische Lösungsansätze 3 Martingal-Ansatz 4 Markovketten-Ansatz 5 Asymptotische Interpretationen 6 Bezug zur Praxis 7 Résumé Anhang Literaturverzeichnis
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 05 
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49595
ER  - 
TY  - INPR
A1  - Paneah, Boris
T1  - Dynamic methods in the general theory of cauchy type functional equations
N2  - Contents: 1 Introduction. Denfitions and Discussions 2 Solvability of the Cauchy Type Functional Equations 2.1 The Case of a P-configuration 2.2 The Case of a Z-configuration 2.3 Multiplicative Cauchy type functional equations 3 Problems in Analysis Reducing to Cauchy Type Functional Equations 3.1 Some problems in Integral Geometry and Cauchy Functional Equations 3.2 First Boundary Problem for Hyperbolic Differential Equations and Cauchy Type Functional Equations 4 Functional Equations Determining Polynomials
T3  - Preprint - (2002) 10 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26295
ER  - 
TY  - INPR
A1  - Karp, Lavi
T1  - On the well-posedness of the vacuum Einstein's equations
N2  - The Cauchy problem of the vacuum Einstein's equations aims to find a semimetric g(αβ) of a spacetime with vanishing Ricci curvature Rα,β and prescribed initial data. Under the harmonic gauge condition, the equations Rα,β = 0 are transferred into a system of quasi-linear wave equations which are called the reduced Einstein equations. The initial data for Einstein's equations are a proper Riemannian metric h(αβ) and a second fundamental form K(αβ). A necessary condition for the reduced Einstein equation to satisfy the vacuum equations is that the initial data satisfy Einstein constraint equations. Hence the data (h(αβ),K(αβ)) cannot serve as initial data for the reduced Einstein equations. Previous results in the case of asymptotically flat spacetimes provide a solution to the constraint equations in one type of Sobolev spaces, while initial data for the evolution equations belong to a different type of Sobolev spaces. The goal of our work is to resolve this incompatibility and to show that under the harmonic gauge the vacuum Einstein equations are well-posed in one type of Sobolev spaces.
T3  - Preprint - (2009) 06 
Y1  - 2009
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-36593
ER  - 
TY  - INPR
A1  - Champagnat, Nicolas
A1  - Roelly, Sylvie
T1  - Limit theorems for conditioned multitype Dawson-Watanabe processes
N2  - 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.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2007, 01 
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49426
ER  - 
TY  - INPR
A1  - Fradon, Myriam
A1  - Roelly, Sylvie
T1  - Infinite system of Brownian Balls: Equilibrium measures are canonical Gibbs
N2  - 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.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2005, 02 
KW  - Stochastic Differential Equation
KW  - hard core potential
KW  - Canonical Gibbs measure
KW  - detailed balance equation
KW  - reversible measure
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51594
ER  - 
TY  - INPR
A1  - Cattiaux, Patrick
A1  - Dai Pra, Paolo
A1  - Poelly, Sylvie
T1  - A constructive approach to a class of ergodic HJB equations with nonsmooth cost
N2  - 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.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2007, 02 
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49430
ER  - 
TY  - INPR
A1  - Läuter, Henning
A1  - Liero, Hannelore
T1  - Nonparametric estimation and testing in survival models
N2  - The aim of this paper is to demonstrate that nonparametric smoothing methods for estimating functions can be an useful tool in the analysis of life time data. After stating some basic notations we will present a data example. Applying standard parametric methods to these data we will see that this approach fails - basic features of the underlying functions are not reflected by their estimates. Our proposal is to use nonparametric estimation methods. These methods are explained in section 2. Nonparametric approaches are better in the sense that they are more flexible, and misspecifications of the model are avoided. But, parametric models have the advantage that the parameters can be interpreted. So, finally, we will formulate a test procedure to check whether a parametric or a nonparametric model is appropriate.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2004, 05 
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51586
ER  - 
TY  - INPR
A1  - Liero, Hannelore
A1  - Liero, Matthias
T1  - Testing the acceleration function in life time models
N2  - The accelerated life time model is considered. First, test procedures for testing the parameter of a parametric acceleration function is investigated; this is done under the assumption of parametric and nonparametric baseline distribution. Further, based on nonparametric estimators for regression functions tests are proposed for checking whether a parametric acceleration function is appropriate to model the influence of the covariates. Resampling procedures are discussed for the realization of these methods. Simulations complete the considerations.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2006, 03 
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49405
ER  - 
TY  - INPR
A1  - Läuter, Henning
T1  - On approximate likelihood in survival models
N2  - We give a common frame for different estimates in survival models. For models with nuisance parameters we approximate the profile likelihood and find estimates especially for the proportional hazard model.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2006, 04 
KW  - Approximate likelihood
KW  - profile likelihood
KW  - propor-tional hazard mode
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-51615
ER  - 
TY  - INPR
A1  - Liero, Hannelore
T1  - A Note on : testing the Copula Based on Densities
N2  - We consider the problem of testing whether the density of a mul- tivariate random variable can be expressed by a prespecified copula function and the marginal densities. The proposed test procedure is based on the asymptotic normality of the properly standardized integrated squared distance between a multivariate kernel density estimator and an estimator of its expectation under the hypothesis. The test of independence is a special case of this approach.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2006, 02 
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49393
ER  - 
TY  - INPR
A1  - Roelly, Sylvie
T1  - Unas propiedades basicas de procesos de ramificación : Lectures held at ICIMAF La Habana, Cuba, 2009 and 2010
N2  - Aus dem Inhalt: 1. Unas propiedades de los procesos de Bienaymé-Galton-Watson de tiempo dis- creto (BGW) 2. Unas propiedades del proceso BGW de tiempo continuo 3. Limites de procesos de BGW cuando la población es numerosa
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2010, 07 
Y1  - 2010
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49620
ER  -