TY - INPR A1 - Chen, Hua A1 - Yu, Chun T1 - Asymptotic behaviour of the trace for Schrödinger operator on fractal drums T3 - Preprint - (2001) 32 Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26157 ER - TY - INPR A1 - Savin, Anton A1 - Sternin, Boris T1 - Index defects in the theory of nonlocal boundary value problems and the η-invariant N2 - The paper deals with elliptic theory on manifolds with boundary represented as a covering space. We compute the index for a class of nonlocal boundary value problems. For a nontrivial covering, the index defect of the Atiyah-Patodi-Singer boundary value problem is computed. We obtain the Poincaré duality in the K-theory of the corresponding manifolds with singularities. T3 - Preprint - (2001) 31 KW - elliptic operator KW - boundary value problem KW - finiteness theorem KW - nonlocal problem KW - covering KW - relative η-invariant KW - index KW - modn-index Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26146 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Sternin, Boris T1 - Some problems of control of semiclassical states for the Schrödinger equation N2 - Contents: Introduction Controlled Quantum Systems The Asymptotic Controllability Problem The Stabilization Problem Unitarily Nonlinear Equations The Quantum Problem The Stabilization Problem for the Schrödinger Equation with a Unitarily Non-linear Control T3 - Preprint - (2001) 30 Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26130 ER - TY - INPR A1 - Messina, Francesca T1 - Local solvability for semilinear Fuchsian equations N2 - Contents: 1 Introduction 2 Differential operators on manifolds with conical singularities 3 When H up(s,y) (B) is an algebra 4 Statement of the main result 5 Proof of the theorem T3 - Preprint - (2001) 29 Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26124 ER - TY - INPR A1 - Harutyunyan, Anahit V. T1 - Toeplitz operators and division theorems in anisotropic spaces of holomorphic functions in the polydisc N2 - This work is an introduction to anisotropic spaces, which have an ω-weight of analytic functions and are generalizations of Lipshitz classes in the polydisc. We prove that these classes form an algebra and are invariant with respect to monomial multiplication. These operators are bounded in these (Lipshitz and Djrbashian) spaces. As an application, we show a theorem about the division by good-inner functions in the mentioned classes is proved. T3 - Preprint - (2001) 28 KW - Toeplitz operators KW - anisotropic spaces KW - polydisc KW - good-inner function Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26110 ER - TY - INPR A1 - Junker, Wolfgang A1 - Schrohe, Elmar T1 - Adiabatic vacuum states on general spacetime manifolds : definition, construction, and physical properties N2 - Adiabatic vacuum states are a well-known class of physical states for linear quantum fields n Robertson-Walker spacetimes. We extend the definition of adiabatic vacua to general spacetime manifolds by using the notion of the Sobolev wavefront set. This definition is also applicable to interacting field theories. Hadamard states form a special subclass of the adiabatic vacua. We analyze physical properties of adiabatic vacuum representations of the Klein-Gordon field on globally hyperbolic spacetme manifolds (factoriality, quasiequivalence, local definteness, Haag duality) and construct them explicitly, if the manifold has a compact Cauchy surface. T3 - Preprint - (2001) 27 Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26100 ER - TY - INPR A1 - Shlapunov, Alexander A1 - Tarkhanov, Nikolai Nikolaevich T1 - Duality by reproducing kernels N2 - Let A be a determined or overdetermined elliptic differential operator on a smooth compact manifold X. Write Ssub(A)(D) for the space of solutions to thesystem Au = 0 in a domain D ⊂ X. Using reproducing kernels related to various Hilbert structures on subspaces of Ssub(A)(D) we show explicit identifications of the dual spaces. To prove the "regularity" of reproducing kernels up to the boundary of D we specify them as resolution operators of abstract Neumann problems. The matter thus reduces to a regularity theorem for the Neumann problem, a well-known example being the ∂-Neumann problem. The duality itself takes place only for those domains D which possess certain convexity properties with respect to A. T3 - Preprint - (2001) 26 Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26095 ER - TY - INPR A1 - Paneah, Boris T1 - On a new problem in integral geometry related to boundary problems for partial differential equations N2 - Contents: 1 Introduction 2 Statement of the problem and definitions 3 The main results 4 Proof of theorem 2 4.1 Reduction of problem (2) to functional - integral equations 4.2 The uniqueness of a solution of equation (2) 4.3 The existence of a solution of equation (2) 5 Proof of theorem 1 6 Proof of theorem 3 7 First boundary problem for hyperbolic differential equations 7.1 Statement of the problem 7.2 The formulation of the result and a sketch of the proof T3 - Preprint - (2001) 25 Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26089 ER - TY - INPR A1 - Galstian, Anahit T1 - Lp - Lq decay estimates for the equation with exponentially growing coefficient N2 - Contents: 1 Introduction 1 Representation formulas 2 Consideration in the pseudodifferential zone: e up(t) |ξ| ≤ 1 3 Consideration in he hyperbolic zone: e up(t) |ξ| ≥ 1 T3 - Preprint - (2001) 24 Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26079 ER - TY - INPR A1 - Witt, Ingo T1 - Asymptotic algebras N2 - The concept of asymptotic type that primarily appears in singular and asymptotic analysis is developed. Especially, asymptotic algebras are introduced. T3 - Preprint - (2001) 23 Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26069 ER -