@article{BoldrighiniFrigioMaponietal.2020, author = {Boldrighini, Carlo and Frigio, Sandro and Maponi, Pierluigi and Pellegrinotti, Alessandro and Sinai, Yakov G.}, title = {3-D incompressible Navier-Stokes equations: Complex blow-up and related real flows}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47220}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472201}, pages = {185 -- 194}, year = {2020}, language = {en} } @article{FigariTeta2020, author = {Figari, Rodolfo and Teta, Alessandro}, title = {Zero-range hamiltonians for three quantum particles}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47218}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472189}, pages = {175 -- 184}, year = {2020}, language = {en} } @article{HrynivWallace2020, author = {Hryniv, Ostap and Wallace, Clare}, title = {Phase separation and sharp large deviations}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47216}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472168}, pages = {155 -- 164}, year = {2020}, language = {en} } @article{JansenKolesnikov2020, author = {Jansen, Sabine and Kolesnikov, Leonid}, title = {Activity expansions for Gibbs correlation functions}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47212}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472121}, pages = {145 -- 154}, year = {2020}, language = {en} } @article{JansenKunaTsagkarogiannis2020, author = {Jansen, Sabine and Kuna, Tobias and Tsagkarogiannis, Dimitrios}, title = {Virial inversion for inhomogeneous systems}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47211}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472111}, pages = {135 -- 144}, year = {2020}, language = {en} } @article{JansenTsagkarogiannis2020, author = {Jansen, Sabine and Tsagkarogiannis, Dimitrios}, title = {Mayer expansion for the Asakura-Oosawa model of colloid theory}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47210}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472109}, pages = {127 -- 134}, year = {2020}, language = {en} } @article{Jursenas2020, author = {Jursenas, Rytis}, title = {The peak model for finite rank supersingular perturbations}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, doi = {10.25932/publishup-47209}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472090}, pages = {117 -- 126}, year = {2020}, language = {en} } @article{KhachatryanNahapetian2020, author = {Khachatryan, Linda and Nahapetian, Boris}, title = {On direct and inverse problems in the description of lattice random fields}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47208}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472083}, pages = {107 -- 116}, year = {2020}, language = {en} } @article{LykovMalyshev2020, author = {Lykov, Alexander and Malyshev, Vadim}, title = {When bounded chaos becomes unbounded}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47206}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472060}, pages = {97 -- 106}, year = {2020}, language = {en} } @article{PecherskyPirogovYambartsev2020, author = {Pechersky, Eugeny and Pirogov, Sergei and Yambartsev, Anatoly}, title = {Large emissions}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47204}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472049}, pages = {77 -- 86}, year = {2020}, language = {en} } @article{PiatnitskiZhizhina2020, author = {Piatnitski, Andrey and Zhizhina, Elena}, title = {Non-local convolution type parabolic equations with fractional and regular time derivative}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47202}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472024}, pages = {65 -- 67}, year = {2020}, language = {en} } @article{PoghosyanZessin2020, author = {Poghosyan, Suren and Zessin, Hans}, title = {Construction of limiting Gibbs processes and the uniqueness of Gibbs processes}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47201}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472015}, pages = {55 -- 64}, year = {2020}, language = {en} } @article{Rafler2020, author = {Rafler, Mathias}, title = {Pinned Gibbs processes}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47200}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-472007}, pages = {45 -- 53}, year = {2020}, language = {en} } @article{SukiasyanMelkonyan2020, author = {Sukiasyan, Hayk and Melkonyan, Tatev}, title = {Semi-recursive algorithm of piecewise linear approximation of two-dimensional function by the method of worst segment dividing}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47198}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-471982}, pages = {35 -- 44}, year = {2020}, language = {en} } @article{Zagrebnov2020, author = {Zagrebnov, Valentin}, title = {Trotter product formula on Hilbert and Banach spaces for operator-norm convergence}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-485-2}, issn = {2199-4951}, doi = {10.25932/publishup-47197}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-471971}, pages = {23 -- 34}, year = {2020}, language = {en} } @article{TillmannKroemkerHornetal.2018, author = {Tillmann, Alexander and Kr{\"o}mker, Detlef and Horn, Florian and Gattinger, Thorsten}, title = {Analysing \& Predicting Students Performance in an Introductory Computer Science Course}, series = {Commentarii informaticae didacticae}, journal = {Commentarii informaticae didacticae}, number = {12}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-416307}, pages = {29 -- 45}, year = {2018}, abstract = {Students of computer science studies enter university education with very different competencies, experience and knowledge. 145 datasets collected of freshmen computer science students by learning management systems in relation to exam outcomes and learning dispositions data (e. g. student dispositions, previous experiences and attitudes measured through self-reported surveys) has been exploited to identify indicators as predictors of academic success and hence make effective interventions to deal with an extremely heterogeneous group of students.}, language = {en} } @book{Pilipenko2014, author = {Pilipenko, Andrey}, title = {An introduction to stochastic differential equations with reflection}, series = {Lectures in pure and applied mathematics}, journal = {Lectures in pure and applied mathematics}, number = {1}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, isbn = {978-3-86956-297-1}, issn = {2199-4951}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-70782}, publisher = {Universit{\"a}t Potsdam}, pages = {ix, 75}, year = {2014}, abstract = {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.}, language = {en} } @unpublished{RoellyRuszel2013, author = {Roelly, Sylvie and Ruszel, Wioletta M.}, title = {Propagation of Gibbsianness for infinite-dimensional diffusions with space-time interaction}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-69014}, year = {2013}, abstract = {We consider infinite-dimensional diffusions where the interaction between the coordinates has a finite extent both in space and time. In particular, it is not supposed to be smooth or Markov. The initial state of the system is Gibbs, given by a strong summable interaction. If the strongness of this initial interaction is lower than a suitable level, and if the dynamical interaction is bounded from above in a right way, we prove that the law of the diffusion at any time t is a Gibbs measure with absolutely summable interaction. The main tool is a cluster expansion in space uniformly in time of the Girsanov factor coming from the dynamics and exponential ergodicity of the free dynamics to an equilibrium product measure.}, 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{LyTarkhanov2013, author = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich}, title = {Generalised Beltrami equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-67416}, year = {2013}, abstract = {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.}, language = {en} } @unpublished{ShlapunovTarkhanov2013, author = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Sturm-Liouville problems in domains with non-smooth edges}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-67336}, year = {2013}, abstract = {We consider a (generally, non-coercive) mixed boundary value problem in a bounded domain for a second order elliptic differential operator A. The differential operator is assumed to be of divergent form and the boundary operator B is of Robin type. The boundary is assumed to be a Lipschitz surface. Besides, we distinguish a closed subset of the boundary and control the growth of solutions near this set. We prove that the pair (A,B) induces a Fredholm operator L in suitable weighted spaces of Sobolev type, the weight function being a power of the distance to the singular set. Moreover, we prove the completeness of root functions related to L.}, 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{KiselevTarkhanov2013, author = {Kiselev, Oleg and Tarkhanov, Nikolai Nikolaevich}, title = {The capture of a particle into resonance at potential hole with dissipative perturbation}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-64725}, year = {2013}, abstract = {We study the capture of a particle into resonance at a potential hole with dissipative perturbation and periodic outside force. The measure of resonance solutions is evaluated. We also derive an asymptotic formula for the parameter range of those solutions which are captured into resonance.}, language = {en} } @unpublished{LeonardRoellyZambrini2013, author = {L{\´e}onard, Christian and Roelly, Sylvie and Zambrini, Jean-Claude}, title = {Temporal symmetry of some classes of stochastic processes}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-64599}, year = {2013}, abstract = {In this article we analyse the structure of Markov processes and reciprocal processes to underline their time symmetrical properties, and to compare them. Our originality consists in adopting a unifying approach of reciprocal processes, independently of special frameworks in which the theory was developped till now (diffusions, or pure jump processes). This leads to some new results, too.}, language = {en} } @unpublished{Roelly2013, author = {Roelly, Sylvie}, title = {Reciprocal processes : a stochastic analysis approach}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-64588}, year = {2013}, abstract = {Reciprocal processes, whose concept can be traced back to E. Schr{\"o}dinger, 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. L{\´e}onard.}, language = {en} } @unpublished{NehringPoghosyanZessin2013, author = {Nehring, Benjamin and Poghosyan, Suren and Zessin, Hans}, title = {On the construction of point processes in statistical mechanics}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-64080}, year = {2013}, abstract = {By means of the cluster expansion method we show that a recent result of Poghosyan and Ueltschi (2009) combined with a result of Nehring (2012) yields a construction of point processes of classical statistical mechanics as well as processes related to the Ginibre Bose gas of Brownian loops and to the dissolution in R^d of Ginibre's Fermi-Dirac gas of such loops. The latter will be identified as a Gibbs perturbation of the ideal Fermi gas. On generalizing these considerations we will obtain the existence of a large class of Gibbs perturbations of the so-called KMM-processes as they were introduced by Nehring (2012). Moreover, it is shown that certain "limiting Gibbs processes" are Gibbs in the sense of Dobrushin, Lanford and Ruelle if the underlying potential is positive. And finally, Gibbs modifications of infinitely divisible point processes are shown to solve a new integration by parts formula if the underlying potential is positive.}, language = {en} } @unpublished{Keller2013, author = {Keller, Peter}, title = {Mathematical modeling of molecular motors}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-63045}, year = {2013}, abstract = {Amongst the many complex processes taking place in living cells, transport of cargoes across the cytosceleton is fundamental to cell viability and activity. To move cargoes between the different cell parts, cells employ Molecular Motors. The motors operate by transporting cargoes along the so-called cellular micro-tubules, namely rope-like structures that connect, for instance, the cell-nucleus and outer membrane. We introduce a new Markov Chain, the killed Quasi-Random-Walk, for such transport molecules and derive properties like the maximal run length and time. Furthermore we introduce permuted balance, which is a more flexible extension of the ordinary reversibility and introduce the notion of Time Duality, which compares certain passage times pathwise. We give a number of sufficient conditions for Time Duality based on the geometry of the transition graph. Both notions are closely related to properties of the killed Quasi-Random-Walk.}, language = {en} } @book{Liero2010, author = {Liero, Hannelore}, title = {Estimation and testing the effect of covariates in accelerated life time models under censoring}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-52823}, publisher = {Universit{\"a}t Potsdam}, year = {2010}, abstract = {The accelerated lifetime model is considered. To test the influence of the covariate we transform the model in a regression model. Since censoring is allowed this approach leads to a goodness-of-fit problem for regression functions under censoring. So nonparametric estimation of regression functions under censoring is investigated, a limit theorem for a L2-distance is stated and a test procedure is formulated. Finally a Monte Carlo procedure is proposed.}, language = {en} } @book{DereudreRoelly2004, author = {Dereudre, David and Roelly, Sylvie}, title = {On Gibbsianness of infinite-dimensional diffusions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-52630}, publisher = {Universit{\"a}t Potsdam}, year = {2004}, abstract = {We analyse different Gibbsian properties of interactive Brownian diffusions X indexed by the lattice \$Z^{d} : X = (X_{i}(t), i ∈ Z^{d}, t ∈ [0, T], 0 < T < +∞)\$. In a first part, these processes are characterized as Gibbs states on path spaces of the form \$C([0, T],R)Z^{d}\$. In a second part, we study the Gibbsian character on \$R^{Z}^{d}\$ of \$v^{t}\$, the law at time t of the infinite-dimensional diffusion X(t), when the initial law \$v = v^{0}\$ is Gibbsian.}, language = {en} } @unpublished{Murr2011, author = {Murr, R{\"u}diger}, title = {Characterization of L{\´e}vy Processes by a duality formula and related results}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-43538}, year = {2011}, abstract = {Processes with independent increments are characterized via a duality formula, including Malliavin derivative and difference operators. This result is based on a characterization of infinitely divisible random vectors by a functional equation. A construction of the difference operator by a variational method is introduced and compared to approaches used by other authors for L´evy processes involving the chaos decomposition. Finally we extend our method to characterize infinitely divisible random measures.}, language = {en} } @unpublished{Penisson2010, author = {P{\´e}nisson, Sophie}, title = {Conditional Limit Theorems for Multitype Branching Processes and Illustration in Epidemiological Risk Analysis}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49589}, year = {2010}, abstract = {This thesis is concerned with the issue of extinction of populations composed of different types of individuals, and their behavior before extinction and in case of a very late extinction. We approach this question firstly from a strictly probabilistic viewpoint, and secondly from the standpoint of risk analysis related to the extinction of a particular model of population dynamics. In this context we propose several statistical tools. The population size is modeled by a branching process, which is either a continuous-time multitype Bienaym{\´e}-Galton-Watson process (BGWc), or its continuous-state counterpart, the multitype Feller diffsion process. We are interested in different kinds of conditioning on nonextinction, and in the associated equilibrium states. These ways of conditioning have been widely studied in the monotype case. However the literature on multitype processes is much less extensive, and there is no systematic work establishing connections between the results for BGWc processes and those for Feller diffusion processes. In the first part of this thesis, we investigate the behavior of the population before its extinction by conditioning the associated branching process Xt on non-extinction (Xt 6= 0), or more generally on non-extinction in a near future 0 < 1 (Xt+ 0 = 0), and by letting t tend to infinity. We prove the result, new in the multitype framework and for 0 > 0, that this limit exists and is nondegenerate. This re ects a stationary behavior for the dynamics of the population conditioned on non-extinction, and provides a generalization of the so-called Yaglom limit, corresponding to the case 0 = 0. In a second step we study the behavior of the population in case of a very late extinction, obtained as the limit when 0 tends to infinity of the process conditioned by Xt+ 0 = 0. The resulting conditioned process is a known object in the monotype case (sometimes referred to as Q-process), and has also been studied when Xt is a multitype Feller diffusion process. We investigate the not yet considered case where Xt is a multitype BGWc process and prove the existence of the associated Q-process. In addition, we examine its properties, including the asymptotic ones, and propose several interpretations of the process. Finally, we are interested in interchanging the limits in t and 0, as well as in the not yet studied commutativity of these limits with respect to the high-density-type relationship between BGWc processes and Feller processes. We prove an original and exhaustive list of all possible exchanges of limit (long-time limit in t, increasing delay of extinction 0, diffusion limit). The second part of this work is devoted to the risk analysis related both to the extinction of a population and to its very late extinction. We consider a branching population model (arising notably in the epidemiological context) for which a parameter related to the first moments of the offspring distribution is unknown. We build several estimators adapted to different stages of evolution of the population (phase growth, decay phase, and decay phase when extinction is expected very late), and prove moreover their asymptotic properties (consistency, normality). In particular, we build a least squares estimator adapted to the Q-process, allowing a prediction of the population development in the case of a very late extinction. This would correspond to the best or to the worst-case scenario, depending on whether the population is threatened or invasive. These tools enable us to study the extinction phase of the Bovine Spongiform Encephalopathy epidemic in Great Britain, for which we estimate the infection parameter corresponding to a possible source of horizontal infection persisting after the removal in 1988 of the major route of infection (meat and bone meal). This allows us to predict the evolution of the spread of the disease, including the year of extinction, the number of future cases and the number of infected animals. In particular, we produce a very fine analysis of the evolution of the epidemic in the unlikely event of a very late extinction.}, language = {en} } @unpublished{NehringZessin2010, author = {Nehring, Benjamin and Zessin, Hans}, title = {A path integral representation of the moment measures of the general ideal Bose gas}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49635}, year = {2010}, abstract = {We reconsider the fundamental work of Fichtner ([2]) and exhibit the permanental structure of the ideal Bose gas again, using another approach which combines a characterization of infinitely divisible random measures (due to Kerstan,Kummer and Matthes [5, 6] and Mecke [8, 9]) with a decomposition of the moment measures into its factorial measures due to Krickeberg [4]. To be more precise, we exhibit the moment measures of all orders of the general ideal Bose gas in terms of certain path integrals. This representation can be considered as a point process analogue of the old idea of Symanzik [11] that local times and self-crossings of the Brownian motion can be used as a tool in quantum field theory. Behind the notion of a general ideal Bose gas there is a class of infinitely divisible point processes of all orders with a Levy-measure belonging to some large class of measures containing the one of the classical ideal Bose gas considered by Fichtner. It is well known that the calculation of moments of higher order of point processes are notoriously complicated. See for instance Krickeberg's calculations for the Poisson or the Cox process in [4].}, language = {en} } @unpublished{Zessin2010, author = {Zessin, Hans}, title = {Classical Symmetric Point Processes : Lectures held at ICIMAF, La Habana, Cuba, 2010}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49619}, year = {2010}, abstract = {The aim of these lectures is a reformulation and generalization of the fundamental investigations of Alexander Bach [2, 3] on the concept of probability in the work of Boltzmann [6] in the language of modern point process theory. The dominating point of view here is its subordination under the disintegration theory of Krickeberg [14]. This enables us to make Bach's consideration much more transparent. Moreover the point process formulation turns out to be the natural framework for the applications to quantum mechanical models.}, language = {en} } @unpublished{Penisson2010, author = {P{\´e}nisson, Sophie}, title = {Estimation of the infection parameter in the different phases of an epidemic modeled by a branching process}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49607}, year = {2010}, abstract = {The aim of this paper is to build and compare estimators of the infection parameter in the different phases of an epidemic (growth and extinction phases). The epidemic is modeled by a Markovian process of order d > 1 (allowing non-Markovian life spans), and can be written as a multitype branching process. We propose three estimators suitable for the different classes of criticality of the process, in particular for the subcritical case corresponding to the extinction phase. We prove their consistency and asymptotic normality for two asymptotics, when the number of ancestors (resp. number of generations) tends to infinity. We illustrate the asymptotic properties with simulated examples, and finally use our estimators to study the infection intensity in the extinction phase of the BSE epidemic in Great-Britain.}, 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{Penisson2009, author = {P{\´e}nisson, Sophie}, title = {Continuous-time multitype branching processes conditioned on very late extinction}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49548}, year = {2009}, abstract = {Multitype branching processes and Feller diffusion processes are conditioned on very late extinction. The conditioned laws are expressed as Doob h-transforms of the unconditioned laws, and an interpretation of the conditioned paths for the branching process is given, via the immortal particle. We study different limits for the conditioned process (increasing delay of extinction, long-time behavior, scaling limit) and provide an exhaustive list of exchangeability results.}, language = {en} } @unpublished{Rafler2009, author = {Rafler, Mathias}, title = {Gaussian loop- and polya processes : a point process approach}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51638}, year = {2009}, abstract = {Zuf{\"a}llige Punktprozesse beschreiben eine (zuf{\"a}llige) zeitliche Abfolge von Ereignissen oder eine (zuf{\"a}llige) r{\"a}umliche Anordnung von Objekten. Deren wichtigster Vertreter ist der Poissonprozess. Der Poissonprozess zum Intensit{\"a}tsmaß, das Lebesgue-Maß ordnet jedem Gebiet sein Volumen zu, erzeugt lokal, d.h in einem beschr{\"a}nkten Gebiet B, gerade eine mit dem Volumen von B poissonverteilte Anzahl von Punkten, die identisch und unabh{\"a}ngig voneinander in B plaziert werden; im Mittel ist diese Anzahl (B). Ersetzt man durch ein Vielfaches a, so wird diese Anzahl mit dem a-fachen Mittelwert erzeugt. Poissonprozesse, die im gesamten Raum unendlich viele Punkte realisieren, enthalten bereits in einer einzigen Stichprobe gen{\"u}gend Informationen, um Statistik betreiben zu k{\"o}nnen: Bedingt man lokal bzgl. der Anzahl der Teilchen einer Stichprobe, so fragt man nach allen Punktprozessen, die eine solche Beobachtung h{\"a}tten liefern k{\"o}nnen. Diese sind Limespunktprozesse zu dieser Beobachtung. Kommt mehr als einer in Frage, spricht man von einem Phasen{\"u}bergang. Da die Menge dieser Limespunktprozesse konvex ist, fragt man nach deren Extremalpunkten, dem Rand. Im ersten Teil wird ein Poissonprozess f{\"u}r ein physikalisches Teilchenmodell f{\"u}r Bosonen konstruiert. Dieses erzeugt sogenannte Loops, das sind geschlossene Polygonz{\"u}ge, die dadurch charakterisiert sind, dass man an einem Ort mit einem Punkt startet, den mit einem normalverteilten Schritt l{\"a}uft und dabei nach einer gegebenen, aber zuf{\"a}lligen Anzahl von Schritten zum Ausgangspunkt zur{\"u}ckkehrt. F{\"u}r verschiedene Beobachtungen von Stichproben werden zugeh{\"o}rige Limespunktprozesse diskutiert. Diese Beobachtungen umfassen etwa das Z{\"a}hlen der Loops gem{\"a}aß ihrer L{\"a}nge, das Z{\"a}hlen der Loops insgesamt, oder das Z{\"a}hlen der von den Loops gemachten Schritte. Jede Wahl zieht eine charakteristische Struktur der invarianten Punktprozesse nach sich. In allen hiesigen F{\"a}llen wird ein charakteristischer Phasen{\"u}bergang gezeigt und Extremalpunkte werden als spezielle Poissonprozesse identifiziert. Insbesondere wird gezeigt, wie die Wahl der Beobachtung die L{\"a}nge der Loops beeinflusst. Geometrische Eigenschaften dieser Poissonprozesse sind der Gegenstand des zweiten Teils der Arbeit. Die Technik der Palmschen Verteilungen eines Punktprozesses erlaubt es, unter den unendlich vielen Loops einer Realisierung den typischen Loop herauszupicken, dessen Geometrie dann untersucht wird. Eigenschaften sind unter anderem die euklidische L{\"a}nge eines Schrittes oder, nimmt man mehrere aufeinander folgende Schritte, das Volumen des von ihnen definierten Simplex. Weiterhin wird gezeigt, dass der Schwerpunkt eines typischen Loops normalverteilt ist mit einer festen Varianz. Der dritte und letzte Teil befasst sich mit der Konstruktion, den Eigenschaften und der Statistik eines neuartigen Punktprozesses, der Polyascher Summenprozess genannt wird. Seine Konstruktion verallgemeinert das Prinzip der Polyaschen Urne: Im Gegensatz zum Poissonprozess, der alle Punkte unabh{\"a}ngig und vor allem identisch verteilt, werden hier die Punkte nacheinander derart verteilt, dass der Ort, an dem ein Punkt plaziert wird, eine Belohnung auf die Wahrscheinlichkeit bekommt, nach der nachfolgende Punkte verteilt werden. Auf diese Weise baut der Polyasche Summenprozess "T{\"u}rmchen", indem sich verschiedene Punkte am selben Ort stapeln. Es wird gezeigt, dass dennoch grundlegende Eigenschaften mit denjenigen des Poissonprozesses {\"u}bereinstimmen, dazu geh{\"o}ren unendliche Teilbarkeit sowie Unabh{\"a}ngigkeit der Zuw{\"a}chse. Zudem werden sein Laplace-Funktional sowie seine Palmsche Verteilung bestimmt. Letztere zeigt, dass die H{\"o}he der T{\"u}rmchen gerade geometrisch verteilt ist. Abschließend werden wiederum Statistiken, nun f{\"u}r den Summenprozess, diskutiert. Je nach Art der Beobachtung von der Stichprobe, etwa Anzahl, Gesamth{\"o}he der T{\"u}rmchen oder beides, gibt es in jedem der drei F{\"a}lle charakteristische Limespunktprozesse und es stellt sich heraus, dass die zugeh{\"o}rigen Extremalverteilungen wiederum Polyasche Summenprozesse sind.}, language = {en} } @unpublished{LouisRouquier2009, author = {Louis, Pierre-Yves and Rouquier, Jean-Baptiste}, title = {Time-to-Coalescence for interacting particle systems : parallel versus sequential updating}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49454}, year = {2009}, abstract = {Studying the influence of the updating scheme for MCMC algorithm on spatially extended models is a well known problem. For discrete-time interacting particle systems we study through simulations the effectiveness of a synchronous updating scheme versus the usual sequential one. We compare the speed of convergence of the associated Markov chains from the point of view of the time-to-coalescence arising in the coupling-from-the-past algorithm. Unlike the intuition, the synchronous updating scheme is not always the best one. The distribution of the time-to-coalescence for these spatially extended models is studied too.}, 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{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{Laeuter2006, author = {L{\"a}uter, Henning}, title = {On approximate likelihood in survival models}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51615}, year = {2006}, abstract = {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.}, language = {en} } @unpublished{LieroLiero2006, author = {Liero, Hannelore and Liero, Matthias}, title = {Testing the acceleration function in life time models}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49405}, year = {2006}, abstract = {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.}, language = {en} } @unpublished{Liero2006, author = {Liero, Hannelore}, title = {A Note on : testing the Copula Based on Densities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-49393}, year = {2006}, abstract = {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.}, 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{LaeuterLiero2004, author = {L{\"a}uter, Henning and Liero, Hannelore}, title = {Nonparametric estimation and testing in survival models}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51586}, year = {2004}, abstract = {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.}, language = {en} } @unpublished{Louis2004, author = {Louis, Pierre-Yves}, title = {Increasing Coupling of Probabilistic Cellular Automata}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51578}, year = {2004}, abstract = {We give a necessary and sufficient condition for the existence of an increasing coupling of N (N >= 2) synchronous dynamics on S-Zd (PCA). Increasing means the coupling preserves stochastic ordering. We first present our main construction theorem in the case where S is totally ordered; applications to attractive PCAs are given. When S is only partially ordered, we show on two examples that a coupling of more than two synchronous dynamics may not exist. We also prove an extension of our main result for a particular class of partially ordered spaces.}, language = {en} } @unpublished{Louis2004, author = {Louis, Pierre-Yves}, title = {Coupling, space and time Mixing for parallel stochastic dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51560}, year = {2004}, abstract = {We first introduce some coupling of a finite number of Probabilistic Cellular Automata dynamics (PCA), preserving the stochastic ordering. Using this tool, for a general attractive probabilistic cellular automata on SZd, where S is finite, we prove that a condition (A) is equivalent to the (time-) convergence towards equilibrium of this Markovian parallel dynamics, in the uniform norm, exponentially fast. This condition (A) means the exponential decay of the influence from the boundary for the invariant measures of the system restricted to finite 'box'-volume. For a class of reversible PCA dynamics on {-1, +1}Zd , with a naturally associated Gibbsian potential ϕ, we prove that a Weak Mixing condition for ϕ implies the validity of the assumption (A); thus the 'exponential ergodicity' of the dynamics towards the unique Gibbs measure associated to ϕ holds. On some particular examples of this PCA class, we verify that our assumption (A) is weaker than the Dobrushin-Vasershtein ergodicity condition. For some special PCA, the 'exponential ergodicity' holds as soon as there is no phase transition.}, language = {en} } @unpublished{Liero2003, author = {Liero, Hannelore}, title = {Testing the Hazard Rate, Part I}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51510}, year = {2003}, abstract = {We consider a nonparametric survival model with random censoring. To test whether the hazard rate has a parametric form the unknown hazard rate is estimated by a kernel estimator. Based on a limit theorem stating the asymptotic normality of the quadratic distance of this estimator from the smoothed hypothesis an asymptotic ®-test is proposed. Since the test statistic depends on the maximum likelihood estimator for the unknown parameter in the hypothetical model properties of this parameter estimator are investigated. Power considerations complete the approach.}, language = {en} } @unpublished{Laeuter2003, author = {L{\"a}uter, Henning}, title = {Estimation in partly parametric additive Cox models}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51509}, year = {2003}, abstract = {The dependence between survival times and covariates is described e.g. by proportional hazard models. We consider partly parametric Cox models and discuss here the estimation of interesting parameters. We represent the ma- ximum likelihood approach and extend the results of Huang (1999) from linear to nonlinear parameters. Then we investigate the least squares esti- mation and formulate conditions for the a.s. boundedness and consistency of these estimators.}, language = {en} } @unpublished{Liero2003, author = {Liero, Hannelore}, title = {Goodness of Fit Tests of L2-Type}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-51494}, year = {2003}, abstract = {We give a survey on procedures for testing functions which are based on quadratic deviation measures. The following problems are considered: Testing whether a density function lies in a parametric class of functions, whether continuous random variables are independent; testing cell probabilities and independence in sparse data sets; testing the parametric fit of a regression homoscedasticity in a regression model and testing the hazard rate in survival models with censoring and with and without covariates.}, language = {en} } @misc{Reich1995, author = {Reich, Sebastian}, title = {On the local qualitative behavior of differential-algebraic equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-46739}, year = {1995}, abstract = {A theoretical famework for the investigation of the qualitative behavior of differential-algebraic equations (DAEs) near an equilibrium point is established. The key notion of our approach is the notion of regularity. A DAE is called regular locally around an equilibrium point if there is a unique vector field such that the solutions of the DAE and the vector field are in one-to-one correspondence in a neighborhood of this equili Drium point. Sufficient conditions for the regularity of an equilibrium point are stated. This in turn allows us to translate several local results, as formulated for vector fields, to DAEs that are regular locally around a g: ven equilibrium point (e.g. Local Stable and Unstable Manifold Theorem, Hopf theorem). It is important that ihese theorems are stated in terms of the given problem and not in terms of the corresponding vector field.}, language = {en} } @misc{Reich1991, author = {Reich, Sebastian}, title = {On an existence and uniqueness theory for nonlinear differential-algebraic equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-46706}, year = {1991}, abstract = {An existence and uniqueness theory is developed for general nonlinear and nonautonomous differential-algebraic equations (DAEs) by exploiting their underlying differential-geometric structure. A DAE is called regular if there is a unique nonautonomous vector field such that the solutions of the DAE and the solutions of the vector field are in one-to-one correspondence. Sufficient conditions for regularity of a DAE are derived in terms of constrained manifolds. Based on this differential-geometric characterization, existence and uniqueness results are stated for regular DAEs. Furthermore, our not ons are compared with techniques frequently used in the literature such as index and solvability. The results are illustrated in detail by means of a simple circuit example.}, language = {en} } @misc{Reich1990, author = {Reich, Sebastian}, title = {On a geometrical interpretation of differential-algebraic equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-46683}, year = {1990}, abstract = {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.}, language = {en} } @misc{Reich1992, author = {Reich, Sebastian}, title = {Differential-algebraic equations and applications in circuit theory}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-46646}, year = {1992}, abstract = {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.}, language = {en} } @unpublished{HovhannisyanSchulze2010, author = {Hovhannisyan, A. H. and Schulze, Bert-Wolfgang}, title = {On a method for solution of the ordinary differential equations connected with Huygens' equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-45381}, year = {2010}, language = {en} } @unpublished{MaSchulze2009, author = {Ma, L. and Schulze, Bert-Wolfgang}, title = {Operators on manifolds with conical singularities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-36608}, year = {2009}, abstract = {We construct elliptic elements in the algebra of (classical pseudo-differential) operators on a manifold M with conical singularities. The ellipticity of any such operator A refers to a pair of principal symbols (σ0, σ1) where σ0 is the standard (degenerate) homogeneous principal symbol, and σ1 is the so-called conormal symbol, depending on the complex Mellin covariable z. The conormal symbol, responsible for the conical singularity, is operator-valued and acts in Sobolev spaces on the base X of the cone. The σ1-ellipticity is a bijectivity condition for all z of real part (n + 1)/2 - γ, n = dimX, for some weight γ. In general, we have to rule out a discrete set of exceptional weights that depends on A. We show that for every operator A which is elliptic with respect to σ0, and for any real weight γ there is a smoothing Mellin operator F in the cone algebra such that A + F is elliptic including σ1. Moreover, we apply the results to ellipticity and index of (operator-valued) edge symbols from the calculus on manifolds with edges.}, language = {en} } @unpublished{Karp2009, author = {Karp, Lavi}, title = {On the well-posedness of the vacuum Einstein's equations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-36593}, year = {2009}, abstract = {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.}, language = {en} } @unpublished{Schulze2009, author = {Schulze, Bert-Wolfgang}, title = {Boundary value problems with the transmission property}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30377}, year = {2009}, abstract = {We give a survey on the calculus of (pseudo-differential) boundary value problems with the transmision property at the boundary, and ellipticity in the Shapiro-Lopatinskij sense. Apart from the original results of the work of Boutet de Monvel we present an approach based on the ideas of the edge calculus. In a final section we introduce symbols with the anti-transmission property.}, language = {en} } @unpublished{AbedSchulze2009, author = {Abed, Jamil and Schulze, Bert-Wolfgang}, title = {Edge-degenerate families of ΨDO's on an infinite cylinder}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30365}, year = {2009}, abstract = {We establish a parameter-dependent pseudo-differential calculus on an infinite cylinder, regarded as a manifold with conical exits to infinity. The parameters are involved in edge-degenerate form, and we formulate the operators in terms of operator-valued amplitude functions.}, language = {en} } @unpublished{Schulze2008, author = {Schulze, Bert-Wolfgang}, title = {The iterative structure of corner operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30353}, year = {2008}, abstract = {We give a brief survey on some new developments on elliptic operators on manifolds with polyhedral singularities. The material essentially corresponds to a talk given by the author during the Conference "Elliptic and Hyperbolic Equations on Singular Spaces", October 27 - 31, 2008, at the MSRI, University of Berkeley.}, 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{Tepoyan2008, author = {Tepoyan, Liparit}, title = {The mixed problem for a degenerate operator equation}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30334}, year = {2008}, abstract = {We consider a mixed problem for a degenerate differentialoperator equation of higher order. We establish some embedding theorems in weighted Sobolev spaces and show existence and uniqueness of the generalized solution of this problem. We also give a description of the spectrum for the corresponding operator.}, language = {en} } @unpublished{Schulze2008, author = {Schulze, Bert-Wolfgang}, title = {On a paper of Krupchyk, Tarkhanov, and Tuomela}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30325}, year = {2008}, language = {en} } @unpublished{SchulzeWei2008, author = {Schulze, Bert-Wolfgang and Wei, Y.}, title = {Edge-boundary problems with singular trace conditions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30317}, year = {2008}, abstract = {The ellipticity of boundary value problems on a smooth manifold with boundary relies on a two-component principal symbolic structure (σψ; σ∂), consisting of interior and boundary symbols. In the case of a smooth edge on manifolds with boundary we have a third symbolic component, namely the edge symbol σ∧, referring to extra conditions on the edge, analogously as boundary conditions. Apart from such conditions in integral form' there may exist singular trace conditions, investigated in [6] on closed' manifolds with edge. Here we concentrate on the phenomena in combination with boundary conditions and edge problem.}, 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{AbedSchulze2008, author = {Abed, Jamil and Schulze, Bert-Wolfgang}, title = {Operators with corner-degenerate symbols}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30299}, year = {2008}, abstract = {We establish elements of a new approch to ellipticity and parametrices within operator algebras on a manifold with higher singularities, only based on some general axiomatic requirements on parameter-dependent operators in suitable scales of spaces. The idea is to model an iterative process with new generations of parameter-dependent operator theories, together with new scales of spaces that satisfy analogous requirements as the original ones, now on a corresponding higher level. The "full" calculus is voluminous; so we content ourselves here with some typical aspects such as symbols in terms of order reducing families, classes of relevant examples, and operators near the conical exit to infinity.}, 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{YagdjianGalstian2007, author = {Yagdjian, Karen and Galstian, Anahit}, title = {Fundamental solutions for wave equation in de Sitter model of universe}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30271}, year = {2007}, abstract = {In this article we construct the fundamental solutions for the wave equation arising in the de Sitter model of the universe. We use the fundamental solutions to represent solutions of the Cauchy problem and to prove the Lp - Lq-decay estimates for the solutions of the equation with and without a source term.}, 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{YinHua2007, author = {Yin, Yang and Hua, Chen}, title = {On chemotaxis systems with saturation growth}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30254}, year = {2007}, abstract = {In this paper, we discuss the global existence of solutions for Chemotaxis models with saturation growth. If the coe±cients of the equations are all positive smooth T-periodic functions, then the problem has a positive T-periodic solution, and meanwhile we discuss here the stability problems for the T-periodic solutions.}, 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{ShlapunovTarkhanov2007, author = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Formal Poincar{\´e} lemma}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30231}, year = {2007}, abstract = {We show how the multiple application of the formal Cauchy-Kovalevskaya theorem leads to the main result of the formal theory of overdetermined systems of partial differential equations. Namely, any sufficiently regular system Au = f with smooth coefficients on an open set U ⊂ Rn admits a solution in smooth sections of a bundle of formal power series, provided that f satisfies a compatibility condition in U.}, language = {en} } @unpublished{Gosson2006, author = {Gosson, Maurice A. de}, title = {Symplectic geometry, Wigner-Weyl-Moyal calculus, and quantum mechanics in phase space}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30212}, year = {2006}, abstract = {Contents: Part I: Symplectic Geometry Chapter 1: Symplectic Spaces and Lagrangian Planes Chapter 2: The Symplectic Group Chapter 3: Multi-Oriented Symplectic Geometry Chapter 4: Intersection Indices in Lag(n) and Sp(n) Part II: Heisenberg Group, Weyl Calculus, and Metaplectic Representation Chapter 5: Lagrangian Manifolds and Quantization Chapter 6: Heisenberg Group and Weyl Operators Chapter 7: The Metaplectic Group Part III: Quantum Mechanics in Phase Space Chapter 8: The Uncertainty Principle Chapter 9: The Density Operator Chapter 10: A Phase Space Weyl Calculus}, language = {en} } @unpublished{Schulze2006, author = {Schulze, Bert-Wolfgang}, title = {Pseudo-differential calculus on manifolds with geometric singularities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30204}, year = {2006}, abstract = {Differential and pseudo-differential operators on a manifold with (regular) geometric singularities can be studied within a calculus, inspired by the concept of classical pseudo-differential operators on a C1 manifold. In the singular case the operators form an algebra with a principal symbolic hierarchy σ = (σj)0≤j≤k, with k being the order of the singularity and σk operator-valued for k ≥ 1. The symbols determine ellipticity and the nature of parametrices. It is typical in this theory that, similarly as in boundary value problems (which are special edge problems, where the edge is just the boundary), there are trace, potential and Green operators, associated with the various strata of the configuration. The operators, obtained from the symbols by various quantisations, act in weighted distribution spaces with multiple weights. We outline some essential elements of this calculus, give examples and also comment on new challenges and interesting problems of the recent development.}, language = {en} } @unpublished{MaergoizTarkhanov2006, author = {Maergoiz, L. and Tarkhanov, Nikolai Nikolaevich}, title = {Optimal recovery from a finite set in Banach spaces of entire functions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30199}, year = {2006}, abstract = {We develop an approach to the problem of optimal recovery of continuous linear functionals in Banach spaces through information on a finite number of given functionals. The results obtained are applied to the problem of the best analytic continuation from a finite set in the complex space Cn, n ≥ 1, for classes of entire functions of exponential type which belong to the space Lp, 1 < p < 1, on the real subspace of Cn. These latter are known as Wiener classes.}, language = {en} } @unpublished{Schulze2006, author = {Schulze, Bert-Wolfgang}, title = {Elliptic differential operators on manifolds with edges}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30188}, year = {2006}, abstract = {On a manifold with edge we construct a specific class of (edgedegenerate) elliptic differential operators. The ellipticity refers to the principal symbolic structure σ = (σψ, σ^) of the edge calculus consisting of the interior and edge symbol, denoted by σψ and σ^, respectively. For our choice of weights the ellipticity will not require additional edge conditions of trace or potential type, and the operators will induce isomorphisms between the respective edge spaces.}, 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{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{Karp2006, author = {Karp, Lavi}, title = {On null quadrature domains}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30156}, year = {2006}, abstract = {The characterization of null quadrature domains in Rn (n ≥ 3) has been an open problem throughout the past two and a half decades. A substantial contribution was done by Friedman and Sakai [10]; they showed that if the complement is bounded, then null quadrature domains are exactly the complement of ellip- soids. The first result with unbounded complements appeared in [15], there it is assumed the complement is contained in an infinitely cylinder. The aim of this paper is to show the relation between null quadrature domains and Newton's theorem on the gravitational force induced by homogeneous homoeoidal ellipsoids. We also succeed to make progress in the classification problem and we show that if the boundary of null quadrature domain is contained in a strip and the complement satisfies a certain capacity condition at infinity, then it must be a half-space or a complement of a strip. In addition, we present a Phragm\Pen-Lindel{\"o}f type theorem which seems to be forgotten in the literature.}, 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{Paneah2006, author = {Paneah, Boris}, title = {Another approach to the stability of linear functional operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30139}, year = {2006}, abstract = {Contents: 1 Introduction. 2 The main notations and notions. 3 Statement of results 4 Proofs of the main results.}, language = {en} } @unpublished{KrupchykTarkhanovTuomela2006, author = {Krupchyk, K. and Tarkhanov, Nikolai Nikolaevich and Tuomela, J.}, title = {Elliptic quasicomplexes in Boutet de Monvel algebra}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30122}, year = {2006}, abstract = {We consider quasicomplexes of Boutet de Monvel operators in Sobolev spaces on a smooth compact manifold with boundary. To each quasicomplex we associate two complexes of symbols. One complex is defined on the cotangent bundle of the manifold and the other on that of the boundary. The quasicomplex is elliptic if these symbol complexes are exact away from the zero sections. We prove that elliptic quasicomplexes are Fredholm. As a consequence of this result we deduce that a compatibility complex for an overdetermined elliptic boundary problem operator is also Fredholm. Moreover, we introduce the Euler characteristic for elliptic quasicomplexes of Boutet de Monvel operators.}, language = {en} } @unpublished{Tarkhanov2006, author = {Tarkhanov, Nikolai Nikolaevich}, title = {Euler characteristic of Fredholm quasicomplexes}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30117}, year = {2006}, abstract = {By quasicomplexes are usually meant perturbations of complexes small in some sense. Of interest are not only perturbations within the category of complexes but also those going beyond this category. A sequence perturbed in this way is no longer a complex, and so it bears no cohomology. We show how to introduce Euler characteristic for small perturbations of Fredholm complexes. The paper is to appear in Funct. Anal. and its Appl., 2006.}, language = {en} } @unpublished{HarutyunyanSchulze2006, author = {Harutyunyan, Gohar and Schulze, Bert-Wolfgang}, title = {Boundary value problems in weighted edge spaces}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30104}, year = {2006}, abstract = {We study elliptic boundary value problems in a wedge with additional edge conditions of trace and potential type. We compute the (difference of the) number of such conditions in terms of the Fredholm index of the principal edge symbol. The task will be reduced to the case of special opening angles, together with a homotopy argument.}, language = {en} } @unpublished{Schulze2006, author = {Schulze, Bert-Wolfgang}, title = {The structure of operators on manifolds with polyhedral singularities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30099}, year = {2006}, abstract = {We discuss intuitive ideas and historical background of concepts in the analysis on configurations with singularities, here in connection with our iterative approach for higher singularities.}, 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{MakhmudovNiyozovTarkhanov2006, author = {Makhmudov, O. and Niyozov, I. and Tarkhanov, Nikolai Nikolaevich}, title = {The cauchy problem of couple-stress elasticity}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30078}, year = {2006}, abstract = {We study the Cauchy problem for the oscillation equation of the couple-stress theory of elasticity in a bounded domain in R3. Both the displacement and stress are given on a part S of the boundary of the domain. This problem is densely solvable while data of compact support in the interior of S fail to belong to the range of the problem. Hence the problem is ill-posed which makes the standard calculi of Fourier integral operators inapplicable. If S is real analytic the Cauchy-Kovalevskaya theorem applies to guarantee the existence of a local solution. We invoke the special structure of the oscillation equation to derive explicit conditions of global solvability and an approximation solution.}, 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{KapanadzeSchulzeSeiler2006, author = {Kapanadze, D. and Schulze, Bert-Wolfgang and Seiler, J.}, title = {Operators with singular trace conditions on a manifold with edges}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30058}, year = {2006}, abstract = {We establish a new calculus of pseudodifferential operators on a manifold with smooth edges and study ellipticity with extra trace and potential conditions (as well as Green operators) at the edge. In contrast to the known scenario with conditions of that kind in integral form we admit in this paper 'singular' trace, potential and Green operators, which are related to the corresponding operators of positive type in Boutet de Monvel's calculus for boundary value problems.}, language = {en} } @unpublished{TarkhanovVasilevski2005, author = {Tarkhanov, Nikolai Nikolaevich and Vasilevski, Nikolai}, title = {Microlocal analysis of the Bochner-Martinelli integral}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30012}, year = {2005}, abstract = {In order to characterise the C*-algebra generated by the singular Bochner-Martinelli integral over a smooth closed hypersurfaces in Cn, we compute its principal symbol. We show then that the Szeg{\"o} projection belongs to the strong closure of the algebra generated by the singular Bochner-Martinelli integral.}, language = {en} } @unpublished{Paneah2005, author = {Paneah, B.}, title = {On the general theory of the cauchy type functional equations with applications in analysis}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30004}, year = {2005}, abstract = {Contents: 1 The main notations and definitions. 2 Statement of the problems and main results. 2.1 The case of a Z-configuration. 2.2 The case of a P-configuration. 3 Proofs of Theorems 1-7. 4 Applications. 4.1 Multiplicative Cauchy type functional equation. 4.2 On some integral equations relating to a geometric problem 4.3 On the solvability of boundary problem for hyperbolic differential equations.}, language = {en} } @unpublished{KrupchykTarkhanovTuomela2005, author = {Krupchyk, K. and Tarkhanov, Nikolai Nikolaevich and Tuomela, J.}, title = {Generalised elliptic boundary problems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29994}, year = {2005}, abstract = {For elliptic systems of differential equations on a manifold with boundary, we prove the Fredholm property of a class of boundary problems which do not satisfy the Shapiro-Lopatinskii property. We name these boundary problems generalised elliptic, for they preserve the main properties of elliptic boundary problems. Moreover, they reduce to systems of pseudodifferential operators on the boundary which are generalised elliptic in the sense of Saks (1997).}, language = {en} } @unpublished{MakhmudovNiyozov2005, author = {Makhmudov, O. I. and Niyozov, I. E.}, title = {Regularization of the Cauchy Problem for the System of Elasticity Theory in R up (m)}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29983}, year = {2005}, abstract = {In this paper we consider the regularization of the Cauchy problem for a system of second order differential equations with constant coefficients.}, 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} } @unpublished{MakhmudovNiyozov2005, author = {Makhmudov, O. I. and Niyozov, I. E.}, title = {The Cauchy problem for the Lame system in infinite domains in R up(m)}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29967}, year = {2005}, abstract = {We consider the problem of analytic continuation of the solution of the multidimensional Lame system in infinite domains through known values of the solution and the corresponding strain tensor on a part of the boundary, i.e,the Cauchy problem.}, language = {en} } @unpublished{MartinSchulze2005, author = {Martin, C.-I. and Schulze, Bert-Wolfgang}, title = {The quantisation of edge symbols}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29959}, year = {2005}, abstract = {We investigate operators on manifolds with edges from the point of view of the symbolic calculus induced by the singularities. We discuss new aspects of the quantisation of edge-degenerate symbols which lead to continuous operators in weighted edge spaces.}, language = {en} } @unpublished{SavinSternin2005, author = {Savin, Anton and Sternin, Boris}, title = {Pseudodifferential subspaces and their applications in elliptic theory}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29937}, year = {2005}, abstract = {The aim of this paper is to explain the notion of subspace defined by means of pseudodifferential projection and give its applications in elliptic theory. Such subspaces are indispensable in the theory of well-posed boundary value problems for an arbitrary elliptic operator, including the Dirac operator, which has no classical boundary value problems. Pseudodifferential subspaces can be used to compute the fractional part of the spectral Atiyah-Patodi-Singer eta invariant, when it defines a homotopy invariant (Gilkey's problem). Finally, we explain how pseudodifferential subspaces can be used to give an analytic realization of the topological K-group with finite coefficients in terms of elliptic operators. It turns out that all three applications are based on a theory of elliptic operators on closed manifolds acting in subspaces.}, language = {en} } @unpublished{AizenbergTarkhanov2005, author = {Aizenberg, Lev A. and Tarkhanov, Nikolai Nikolaevich}, title = {Stable expansions in homogeneous polynomials}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29925}, year = {2005}, abstract = {An expansion for a class of functions is called stable if the partial sums are bounded uniformly in the class. Stable expansions are of key importance in numerical analysis where functions are given up to certain error. We show that expansions in homogeneous functions are always stable on a small ball around the origin, and evaluate the radius of the largest ball with this property.}, language = {en} } @unpublished{Krainer2005, author = {Krainer, Thomas}, title = {Elliptic boundary problems on manifolds with polycylindrical ends}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29912}, year = {2005}, abstract = {We investigate general Shapiro-Lopatinsky elliptic boundary value problems on manifolds with polycylindrical ends. This is accomplished by compactifying such a manifold to a manifold with corners of in general higher codimension, and we then deal with boundary value problems for cusp differential operators. We introduce an adapted Boutet de Monvel's calculus of pseudodifferential boundary value problems, and construct parametrices for elliptic cusp operators within this calculus. Fredholm solvability and elliptic regularity up to the boundary and up to infinity for boundary value problems on manifolds with polycylindrical ends follows.}, language = {en} } @unpublished{KapanadzeSchulze2005, author = {Kapanadze, David and Schulze, Bert-Wolfgang}, title = {Boundary-contact problems for domains with edge singularities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29901}, year = {2005}, abstract = {We study boundary-contact problems for elliptic equations (and systems) with interfaces that have edge singularities. Such problems represent continuous operators between weighted edge spaces and subspaces with asymptotics. Ellipticity is formulated in terms of a principal symbolic hierarchy, containing interior, transmission, and edge symbols. We construct parametrices, show regularity with asymptotics of solutions in weighted edge spaces and illustrate the results by boundary-contact problems for the Laplacian with jumping coefficients.}, language = {en} }