TY - INPR A1 - Bär, Christian A1 - Ginoux, Nicolas T1 - Classical and quantum fields on Lorentzian manifolds N2 - We construct bosonic and fermionic locally covariant quantum fields theories on curved backgrounds for large classes of fields. We investigate the quantum field and n-point functions induced by suitable states. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)15 KW - Wave operator KW - Dirac-type operator KW - globally hyperbolic spacetime KW - Green's operator KW - CCR-algebra Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-59973 ER - TY - INPR A1 - Nehring, Benjamin T1 - Construction of point processes for classical and quantum gases N2 - We propose a new construction of point processes, which generalizes the class of infinitely divisible point processes. Examples are the quantum Boson and Fermion gases as well as the classical Gibbs point processes, where the interaction is given by a stable and regular pair potential. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)14 KW - Gibbs point processes KW - permanental- KW - determinantal point processes KW - cluster expansion KW - Lévy measure KW - infinitely divisible point processes Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-59648 ER - TY - INPR A1 - Rattana, Amornrat A1 - Böckmann, Christine T1 - Matrix methods for computing Eigenvalues of Sturm-Liouville problems of order four N2 - This paper examines and develops matrix methods to approximate the eigenvalues of a fourth order Sturm-Liouville problem subjected to a kind of fixed boundary conditions, furthermore, it extends the matrix methods for a kind of general boundary conditions. The idea of the methods comes from finite difference and Numerov's method as well as boundary value methods for second order regular Sturm-Liouville problems. Moreover, the determination of the correction term formulas of the matrix methods are investigated in order to obtain better approximations of the problem with fixed boundary conditions since the exact eigenvalues for q = 0 are known in this case. Finally, some numerical examples are illustrated. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)13 KW - Finite difference method KW - Numerov's method KW - Boundary value methods KW - Fourth order Sturm-Liouville problem KW - Eigenvalues Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-59279 ER - TY - INPR A1 - Alsaedy, Ammar A1 - Tarkhanov, Nikolai Nikolaevich T1 - Spectral projection for the dbar-Neumann problem N2 - We show that the spectral kernel function of the dbar-Neumann problem on a non-compact strongly pseudoconvex manifold is smooth up to the boundary. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)12 KW - dbar-Neumann problem KW - strongly pseudoconvex domains KW - spectral kernel function Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-58616 SN - 2193-6943 ER - TY - INPR A1 - Tarkhanov, Nikolai Nikolaevich T1 - A simple numerical approach to the Riemann hypothesis N2 - The Riemann hypothesis is equivalent to the fact the the reciprocal function 1/zeta (s) extends from the interval (1/2,1) to an analytic function in the quarter-strip 1/2 < Re s < 1 and Im s > 0. Function theory allows one to rewrite the condition of analytic continuability in an elegant form amenable to numerical experiments. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1 (2012) 9 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-57645 SN - 2193-6943 ER - TY - INPR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - On completeness of root functions of Sturm-Liouville problems with discontinuous boundary operators N2 - We consider a Sturm-Liouville boundary value problem in a bounded domain D of R^n. By this is meant that the differential equation is given by a second order elliptic operator of divergent form in D and the boundary conditions are of Robin type on bD. The first order term of the boundary operator is the oblique derivative whose coefficients bear discontinuities of the first kind. Applying the method of weak perturbation of compact self-adjoint operators and the method of rays of minimal growth, we prove the completeness of root functions related to the boundary value problem in Lebesgue and Sobolev spaces of various types. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)11 KW - Sturm-Liouville problems KW - discontinuous Robin condition KW - root functions KW - Lipschitz domains Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-57759 SN - 2193-6943 ER - TY - INPR A1 - Grudsky, Serguey A1 - Tarkhanov, Nikolai Nikolaevich T1 - Conformal reduction of boundary problems for harmonic functions in a plane domain with strong singularities on the boundary N2 - We consider the Dirichlet, Neumann and Zaremba problems for harmonic functions in a bounded plane domain with nonsmooth boundary. The boundary curve belongs to one of the following three classes: sectorial curves, logarithmic spirals and spirals of power type. To study the problem we apply a familiar method of Vekua-Muskhelishvili which consists in using a conformal mapping of the unit disk onto the domain to pull back the problem to a boundary problem for harmonic functions in the disk. This latter is reduced in turn to a Toeplitz operator equation on the unit circle with symbol bearing discontinuities of second kind. We develop a constructive invertibility theory for Toeplitz operators and thus derive solvability conditions as well as explicit formulas for solutions. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)10 KW - singular integral equations KW - nonsmooth curves KW - boundary value problems Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-57745 ER - TY - INPR A1 - Koppitz, Jörg A1 - Musunthia, Tiwadee T1 - Maximal subsemigroups containing a particular semigroup N2 - We study maximal subsemigroups of the monoid T(X) of all full transformations on the set X = N of natural numbers containing a given subsemigroup W of T(X), where each element of a given set U is a generator of T(X) modulo W. This note continues the study of maximal subsemigroups of the monoid of all full transformations on an infinite set. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1 (2012) 8 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-57465 ER - TY - INPR A1 - Blanchard, Gilles A1 - Mathé, Peter T1 - Discrepancy principle for statistical inverse problems with application to conjugate gradient iteration N2 - The authors discuss the use of the discrepancy principle for statistical inverse problems, when the underlying operator is of trace class. Under this assumption the discrepancy principle is well defined, however a plain use of it may occasionally fail and it will yield sub-optimal rates. Therefore, a modification of the discrepancy is introduced, which takes into account both of the above deficiencies. For a variety of linear regularization schemes as well as for conjugate gradient iteration this modification is shown to yield order optimal a priori error bounds under general smoothness assumptions. A posteriori error control is also possible, however at a sub-optimal rate, in general. This study uses and complements previous results for bounded deterministic noise. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1 (2012) 7 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-57117 ER - TY - INPR A1 - Klein, Markus A1 - Léonard, Christian A1 - Rosenberger, Elke T1 - Agmon-type estimates for a class of jump processes N2 - In the limit we analyze the generators of families of reversible jump processes in the n-dimensional space associated with a class of symmetric non-local Dirichlet forms and show exponential decay of the eigenfunctions. The exponential rate function is a Finsler distance, given as solution of certain eikonal equation. Fine results are sensitive to the rate functions being twice differentiable or just Lipschitz. Our estimates are similar to the semiclassical Agmon estimates for differential operators of second order. They generalize and strengthen previous results on the lattice. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1 (2012) 6 KW - finsler distance KW - decay of eigenfunctions KW - jump process KW - Dirichlet form Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-56995 ER -