TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Nazaikinskii, Vladimir E.
A1  - Sternin, Boris
T1  - On the homotopy classification of elliptic operators on manifolds with singularities
N2  - We study the homotopy classification of elliptic operators on manifolds with singularities and establish necessary and sufficient conditions under which the classification splits into terms corresponding to the principal symbol and the conormal symbol.
T3  - Preprint - (1999) 21 
KW  - elliptic operators
KW  - homotopy classification
KW  - manifold with singularities
KW  - Atiyah-Singer theorem
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25574
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 E.
A1  - Sternin, Boris
T1  - Surgery and the relative index in elliptic theory
N2  - We prove a general theorem on the local property of the relative index 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 as well as for elliptic boundary value problems with a symmetry condition for the conormal symbol.
T3  - Preprint - (1999) 17 
KW  - elliptic operators
KW  - index theory
KW  - surgery
KW  - relative index
KW  - manifold with singularities
KW  - boundary value problems
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25538
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir E.
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Quantization methods in differential equations : Chapter 2: Quantization of Lagrangian modules
N2  - In this chapter we use the wave packet transform described in Chapter 1 to quantize extended classical states represented by so-called Lagrangian sumbanifolds of the phase space. Functions on a Lagrangian manifold form a module over the ring of classical Hamiltonian functions on the phase space (with respect to pointwise multiplication). The quantization procedure intertwines this multiplication with the action of the corresponding quantum Hamiltonians; hence we speak of quantization of Lagrangian modules. The semiclassical states obtained by this quantization procedure provide asymptotic solutions to differential equations with a small parameter. Locally, such solutions can be represented by WKB elements. Global solutions are given by Maslov's canonical operator [2]; also see, e.g., [3] and the references therein. Here the canonical operator is obtained in the framework of the universal quantization procedure provided by the wave packet transform. This procedure was suggested in [4] (see also the references there) and further developed in [5]; our exposition is in the spirit of these papers. Some further bibliographical remarks can be found in the beginning of Chapter 1.
T3  - Preprint - (1999) 22 
Y1  - 1999
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25582
ER  -