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 - Nazaikinskii, Vladimir A1 - Sternin, Boris T1 - On surgery in elliptic theory N2 - We prove a general theorem on the behavior of the relative index under surgery for a wide class of Fredholm operators, including relative index theorems for elliptic operators due to Gromov-Lawson, Anghel, Teleman, Booß-Bavnbek-Wojciechowski, et al. as special cases. In conjunction with additional conditions (like symmetry conditions), this theorem permits one to compute the analytical index of a given operator. In particular, we obtain new index formulas for elliptic pseudodifferential operators and quantized canonical transformations on manifolds with conical singularities. T3 - Preprint - (2000) 22 KW - elliptic operators KW - index theory KW - surgery KW - relative index KW - manifold with singularities Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25873 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Sternin, Boris T1 - Relative elliptic theory N2 - This paper is a survey of relative elliptic theory (i.e. elliptic theory in the category of smooth embeddings), closely related to the Sobolev problem, first studied by Sternin in the 1960s. We consider both analytic aspects to the theory (the structure of the algebra of morphismus, ellipticity, Fredholm property) and topological aspects (index formulas and Riemann-Roch theorems). We also study the algebra of Green operators arising as a subalgebra of the algebra of morphisms. T3 - Preprint - (2002) 23 KW - Sobolev problem KW - elliptic morphism KW - (co)boundary operator KW - Green operator KW - index KW - Riemann-Roch theorem Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26400 ER - TY - INPR A1 - 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 - Nazaikinskii, Vladimir A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris A1 - Shatalov, Victor T1 - A Lefschetz fixed point theorem for manifolds with conical singularities N2 - We establish an Atiyah-Bott-Lefschetz formula for elliptic operators on manifolds with conical singular points. T3 - Preprint - (1997) 20 KW - elliptic operator KW - Fredholm property KW - conical singularities KW - pseudo-diferential operators KW - Lefschetz fixed point formula KW - regularizer Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25073 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris A1 - Shatalov, Victor T1 - Quantization of symplectic transformations on manifolds with conical singularities N2 - The structure of symplectic (canonical) transformations on manifolds with conical singularities is established. The operators associated with these transformations are defined in the weight spaces and their properties investigated. T3 - Preprint - (1997) 23 KW - manifolds with conical singularities KW - symplectic (canonical) transformations KW - quantization KW - Mellin transform Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25084 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Surgery and the relative index theorem for families of elliptic operators N2 - We prove a theorem describing the behaviour of the relative index of families of Fredholm operators under surgery performed on spaces where the operators act. In connection with additional conditions (like symmetry conditions) this theorem results in index formulas for given operator families. By way of an example, we give an application to index theory of families of boundary value problems. T3 - Preprint - (2002) 11 KW - elliptic operators KW - index theory KW - surgery KW - relative index KW - boundary value problems Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26300 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Quantization and the wave packet transform T3 - Preprint - (1999) 08 Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25447 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Quantization methods in differential equations : Chapter 3: Applications of noncommutative analysis to operator algebras on singular manifolds N2 - Content: Chapter 3: Applications of Noncommutative Analysis to Operator Algebras on Singular Manifolds 3.1 Statement of the problem 3.2 Operators on the Model Cone 3.3 Operators on the Model Cusp of Order k 3.4 An Application to the Construction of Regularizers and Proof of the Finiteness Theorem T3 - Preprint - (2000) 15 Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25801 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Quantization methods in differential equations : Chapter 2: Exactly soluble commutation relations (The simplest class of classical mechanics) N2 - Content: Chapter 2: Exactly SolubleCommutation Relations (The Simplest Class of Classical Mechanics) 2.1 Some examples 2.2 Lie commutation relations 2.3 Non-Lie (nonlinear) commutation relations T3 - Preprint - (2000) 14 Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25796 ER -