TY - JOUR A1 - Nazajkinskij, Vladimir E. A1 - Savin, Anton A1 - Sternin, Boris Ju. A1 - Schulze, Bert-Wolfgang T1 - Pseudodifferential operators on manifolds with singularities and localization Y1 - 2005 SN - 1064-5624 ER - TY - JOUR A1 - Savin, Anton A1 - Sternin, Boris T1 - Boundary value problems on manifolds with fibered boundary N2 - We define a class of boundary value problems on manifolds with fibered boundary. This class is in a certain sense a deformation between the classical boundary value problems and the Atiyah-Patodi-Singer problems in subspaces (it contains both as special cases). The boundary conditions in this theory are taken as elements of the C*-algebra generated by pseudodifferential operators and families of pseudodifferential operators in the fibers. We prove the Fredholm. property for elliptic boundary value problems and compute a topological obstruction (similar to Atiyah-Bott obstruction) to the existence of elliptic boundary conditions for a given elliptic operator. Geometric operators with trivial and nontrivial obstruction are given. (c) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Y1 - 2005 SN - 0025-584X ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - The index problem on manifolds with singularities T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2004 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Elliptic theory on manifolds with edges T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2004 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - On the homotopy classification of elliptic operators on manifolds with edges T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2004 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Savin, Anton A1 - Sternin, Boris T1 - Pseudodifferential subspaces and their applications in elliptic theory T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Nazajkinskij, Vladimir E. A1 - Savin, Anton A1 - Sternin, Boris Ju. A1 - Schulze, Bert-Wolfgang T1 - On the index of elliptic operators on manifolds with edges N2 - Necessary and sufficient conditions for the representation of the index of elliptic operators on manifolds with edges in the form of the sum of homotopy invariants of symbols on the smooth stratum and on the edge are found. An index formula is obtained for elliptic operators on manifolds with edges under symmetry conditions with respect to the edge covariables Y1 - 2005 ER - TY - JOUR A1 - Nazajkinskij, Vladimir E. A1 - Savin, Anton A1 - Sternin, Boris Ju. A1 - Schulze, Bert-Wolfgang T1 - Pseudodifferential operators on manifolds with edges Y1 - 2004 SN - 1064-5624 ER - TY - JOUR A1 - Nazajkinskij, Vladimir E. A1 - Savin, Anton A1 - Sternin, Boris Ju. A1 - Schulze, Bert-Wolfgang T1 - On the existence of elliptic problems on manifolds with edges Y1 - 2004 SN - 1064-5624 ER - TY - JOUR A1 - Nazajkinskij, Vladimir E. A1 - Savin, Anton A1 - Sternin, Boris Ju. A1 - Schulze, Bert-Wolfgang T1 - On the index of differential operators on manifolds with edges Y1 - 2004 SN - 1064-5624 ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Localization (surgery) in elliptic theory T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2003 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Elliptic theory on manifolds with nonisolated singularities : 5 Index formulas for elliptic problems on manifolds with edges T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2003 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Index defects in elliptic theory T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2003 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Pseudodifferential Operators T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2003 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Eta Invariant and the Spectral Flow T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2003 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Manifolds with isolated singularities T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2003 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Elliptic theory on manifolds with edges. I T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2003 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Surgery and the relative index theorem for families of elliptic operators T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2002 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Elliptic theory on manifolds with nonisolated singularities : 1 the index of families of cone-degenerate operators T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2002 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Elliptic theory on Manifolds with nonisolated singularities : 3 the Spectral flow of Families of conaormal symbols T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2002 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Elliptic theory on manifolds with nonisolated singularities : 4 obstructions to elliptic problems on manifolds with edges T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2002 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Sternin, Boris T1 - Relative elliptic theory T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2002 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Savin, Anton A1 - Sternin, Boris T1 - Eta-invariant and Pontrjagin duality in K-theory N2 - The topological significance of the spectral Atiyah-Patodi-Singer η-invariant is investigated. We show that twice the fractional part of the invariant is computed by the linking pairing in K-theory with the orientation bundle of the manifold. The Pontrjagin duality implies the nondegeneracy of the linking form. An example of a nontrivial fractional part for an even-order operator is presented. T3 - Preprint - (2000) 08 KW - eta-invariant KW - K-theory KW - Pontrjagin duality KW - linking coefficients KW - Atiyah-Patodi-Singer theory KW - modulo n index Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25747 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris A1 - Shatalov, Victor T1 - On the index of differential operators on manifolds with conical singularities N2 - The paper contains the proof of the index formula for manifolds with conical points. For operators subject to an additional condition of spectral symmetry, the index is expressed as the sum of multiplicities of spectral points of the conormal symbol (indicial family) and the integral from the Atiyah-Singer form over the smooth part of the manifold. The obtained formula is illustrated by the example of the Euler operator on a two-dimensional manifold with conical singular point. T3 - Preprint - (1997) 10 KW - conical singularities KW - Mellin transform KW - pseudodiferential operators KW - ellipticity KW - Fredholm operators KW - regularizers KW - analytic index Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-24965 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Nazaikinskii, Vladimir A1 - Sternin, Boris T1 - The index of quantized contact transformations on manifolds with conical singularities N2 - The quantization of contact transformations of the cosphere bundle over a manifold with conical singularities is described. The index of Fredholm operators given by this quantization is calculated. The answer is given in terms of the Epstein-Melrose contact degree and the conormal symbol of the corresponding operator. T3 - Preprint - (1998) 16 KW - manifolds with conical singularities KW - contact transformations KW - quantization KW - ellipticity KW - Fredholm operators KW - regularizers KW - index formulas Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25276 ER - TY - INPR A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - On the invariant index formulas for spectral boundary value problems N2 - In the paper we study the possibility to represent the index formula for spectral boundary value problems as a sum of two terms, the first one being homotopy invariant of the principal symbol, while the second depends on the conormal symbol of the problem only. The answer is given in analytical, as well as in topological terms. T3 - Preprint - (1998) 18 KW - spectral boundary value problems KW - Fredholm property KW - index of elliptic operator KW - Chern character KW - Atiyah-Patodi-Singer theory Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25285 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Nazaikinskii, Vladimir A1 - Sternin, Boris T1 - A semiclassical quantization on manifolds with singularities and the Lefschetz Formula for Elliptic Operators N2 - For general endomorphisms of elliptic complexes on manifolds with conical singularities, the semiclassical asymptotics of the Atiyah-Bott-Lefschetz number is calculated in terms of fixed points of the corresponding canonical transformation of the symplectic space. T3 - Preprint - (1998) 19 KW - elliptic operator KW - Fredholm property KW - conical singularities KW - pseudodiferential operators KW - Lefschetz fixed point formula KW - regularizer Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25296 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris A1 - Shatalov, Victor T1 - Operator algebras on singular manifolds. IV, V T3 - Preprint - (1997) 19 Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25062 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 - Schulze, Bert-Wolfgang A1 - Sternin, Boris A1 - Shatalov, Victor T1 - On general boundary value problems for elliptic equations N2 - We construct a theory of general boundary value problems for differential operators whose symbols do not necessarily satisfy the Atiyah-Bott condition [3] of vanishing of the corresponding obstruction. A condition for these problems to be Fredholm is introduced and the corresponding finiteness theorems are proved. T3 - Preprint - (1997) 35 KW - elliptic boundary value problems KW - Atiyah-Bott condition KW - Calderón projections KW - Cauchy Riemann operator KW - Euler operator Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25138 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Nazaikinskii, Vladimir A1 - Sternin, Boris A1 - Shatalov, Victor T1 - Spectral boundary value problems and elliptic equations on singular manifolds N2 - For elliptic operators on manifolds with boundary, we define spectral boundary value problems, which generalize the Atiyah-Patodi-Singer problem to the case of nonhomogeneous boundary conditions, operators of arbitrary order, and nonself-adjoint conormal symbols. The Fredholm property is proved and equivalence with certain elliptic equations on manifolds with conical singularities is established. T3 - Preprint - (1997) 36 KW - APS problem KW - spectral resolution KW - nonhomogeneous boundary value problems KW - Fredholm property Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25147 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Differential operators on manifolds with singularities : analysis and topology : Chapter 7: The index problem on manifolds with singularities N2 - Contents: Chapter 7: The Index Problemon Manifolds with Singularities Preface 7.1. The Simplest Index Formulas 7.1.1. General properties of the index 7.1.2. The index of invariant operators on the cylinder 7.1.3. Relative index formulas 7.1.4. The index of general operators on the cylinder 7.1.5. The index of operators of the form 1 + G with a Green operator G 7.1.6. The index of operators of the form 1 + G on manifolds with edges 7.1.7. The index on bundles with smooth base and fiber having conical points 7.2. The Index Problem for Manifolds with Isolated Singularities 7.2.1. Statement of the index splitting problem 7.2.2. The obstruction to the index splitting 7.2.3. Computation of the obstruction in topological terms 7.2.4. Examples. Operators with symmetries 7.3. The Index Problem for Manifolds with Edges 7.3.1. The index excision property 7.3.2. The obstruction to the index splitting 7.4. Bibliographical Remarks T3 - Preprint - (2004) 06 Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26700 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Differential operators on manifolds with singularities : analysis and topology : Chapter 4: Pseudodifferential operators N2 - Contents: Chapter 4: Pseudodifferential Operators 4.1. Preliminary Remarks 4.1.1. Why are pseudodifferential operators needed? 4.1.2. What is a pseudodifferential operator? 4.1.3. What properties should the pseudodifferential calculus possess? 4.2. Classical Pseudodifferential Operators on Smooth Manifolds 4.2.1. Definition of pseudodifferential operators on a manifold 4.2.2. Hörmander’s definition of pseudodifferential operators 4.2.3. Basic properties of pseudodifferential operators 4.3. Pseudodifferential Operators in Sections of Hilbert Bundles 4.3.1. Hilbert bundles 4.3.2. Operator-valued symbols. Specific features of the infinite-dimensional case 4.3.3. Symbols of compact fiber variation 4.3.4. Definition of pseudodifferential operators 4.3.5. The composition theorem 4.3.6. Ellipticity 4.3.7. The finiteness theorem 4.4. The Index Theorem 4.4.1. The Atiyah–Singer index theorem 4.4.2. The index theorem for pseudodifferential operators in sections of Hilbert bundles 4.4.3. Proof of the index theorem 4.5. Bibliographical Remarks T3 - Preprint - (2003) 11 Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26587 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Differential operators on manifolds with singularities : analysis and topology : Chapter 3: Eta invariant and the spectral flow N2 - Contents: Chapter 3: Eta Invariant and the Spectral Flow 3.1. Introduction 3.2. The Classical Spectral Flow 3.2.1. Definition and main properties 3.2.2. The spectral flow formula for periodic families 3.3. The Atiyah–Patodi–Singer Eta Invariant 3.3.1. Definition of the eta invariant 3.3.2. Variation under deformations of the operator 3.3.3. Homotopy invariance. Examples 3.4. The Eta Invariant of Families with Parameter (Melrose’s Theory) 3.4.1. A trace on the algebra of parameter-dependent operators 3.4.2. Definition of the Melrose eta invariant 3.4.3. Relationship with the Atiyah–Patodi–Singer eta invariant 3.4.4. Locality of the derivative of the eta invariant. Examples 3.5. The Spectral Flow of Families of Parameter-Dependent Operators 3.5.1. Meromorphic operator functions. Multiplicities of singular points 3.5.2. Definition of the spectral flow 3.6. Higher Spectral Flows 3.6.1. Spectral sections 3.6.2. Spectral flow of homotopies of families of self-adjoint operators 3.6.3. Spectral flow of homotopies of families of parameter-dependent operators 3.7. Bibliographical Remarks T3 - Preprint - (2003) 12 Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26595 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Differential operators on manifolds with singularities : analysis and topology : Chapter 5: Manifolds with isolated singularities N2 - Contents: Chapter 5: Manifolds with Isolated Singularities 5.1. Differential Operators and the Geometry of Singularities 5.1.1. How do isolated singularities arise? Examples 5.1.2. Definition and methods for the description of manifolds with isolated singularities 5.1.3. Bundles. The cotangent bundle 5.2. Asymptotics of Solutions, Function Spaces,Conormal Symbols 5.2.1. Conical singularities 5.2.2. Cuspidal singularities 5.3. A Universal Representation of Degenerate Operators and the Finiteness Theorem 5.3.1. The cylindrical representation 5.3.2. Continuity and compactness 5.3.3. Ellipticity and the finiteness theorem 5.4. Calculus of ΨDO 5.4.1. General ΨDO 5.4.2. The subalgebra of stabilizing ΨDO 5.4.3. Ellipticity and the finiteness theorem T3 - Preprint - (2003) 23 Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26659 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Differential operators on manifolds with singularities : analysis and topology : Chapter 6: Elliptic theory on manifolds with edges N2 - Contents: Chapter 6: Elliptic Theory on Manifolds with Edges Introduction 6.1. Motivation and Main Constructions 6.1.1. Manifolds with edges 6.1.2. Edge-degenerate differential operators 6.1.3. Symbols 6.1.4. Elliptic problems 6.2. Pseudodifferential Operators 6.2.1. Edge symbols 6.2.2. Pseudodifferential operators 6.2.3. Quantization 6.3. Elliptic Morphisms and the Finiteness Theorem 6.3.1. Matrix Green operators 6.3.2. General morphisms 6.3.3. Ellipticity, Fredholm property, and smoothness Appendix A. Fiber Bundles and Direct Integrals A.1. Local theory A.2. Globalization A.3. Versions of the Definition of the Norm T3 - Preprint - (2004) 15 Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26757 ER - TY - INPR A1 - Nazaikinskii, Vladimir E. A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - On the homotopy classification of elliptic operators on manifolds with edges N2 - We obtain a stable homotopy classification of elliptic operators on manifolds with edges. T3 - Preprint - (2004) 16 Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26769 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - Structure rings of singularities and differential equations Y1 - 1997 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - Operator algebras associated with resurgent transforms and differential equations on manifolds with singularities Y1 - 1997 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - Nonstationary problems for Borel-Fuchs type equations Y1 - 1997 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - Resurgent analysis in the theory of differential equations with singularities Y1 - 1995 ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. T1 - The index of quantized contact transformations on manifolds with conical singularities T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1998 VL - 1998, 16 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. T1 - On the invariant index formulas for spectral boundary value problems T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1998 VL - 1998, 18b PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - Differential equations on manifolds with singularities in classes of resurgent functions Y1 - 1998 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - On some global aspects of the theory of partial differential equations on manifolds with singularities Y1 - 1998 ER - TY - JOUR A1 - Nazajkinskij, Vladimir E. A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - Spectral boundary value problems and elliptic equations on singular manifolds Y1 - 1998 ER - TY - BOOK A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - On the index of differential operators on manifolds with conical singularities T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1997 VL - 1997, 10 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - On general boundary value problems for elliptic equations T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1997 VL - 1997, 35 PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - Nonstationary problems for equations of Borel-Fuchs type T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1997 VL - 1997, 11 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - On general boundary value problems for elliptic equations Y1 - 1998 SN - 0368-8666 SN - 0025-5157 SN - 0321-4540 ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. T1 - A semiclassical quantization on manifolds with singularities and the Lefschetz formula for elliptic operators T3 - Preprint / Universität Potsdam, Institut für Mathematik Y1 - 1998 VL - 1998, 19 PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - Resurgent analysis and differential equations with singularities Y1 - 1994 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - On the index of differential operators on manifolds with conical singularities Y1 - 1998 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - An operator algebra on manifolds with cusp type singularities Y1 - 1998 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - On general boundary value problems for elliptic equations Y1 - 1998 ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Sternin, Boris T1 - Some problems of control of semiclassical states for the schrödinger equation T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2001 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Savin, Anton A1 - Sternin, Boris T1 - Index defects in the theorie of nonlocal boundary value problems and the n-invariant T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2001 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Localization Problem in Index Theory of Elliptic Operators T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2001 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Savin, Anton A1 - Sternin, Boris Ju. T1 - Eta invariant and parity conditions T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2000 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. T1 - Noncommutative Analysis and High-Frequency Asymptotics T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2000 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Sternin, Boris Ju. T1 - On surgery in elliptic theory T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2000 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. T1 - Elliptic operators in subspaces T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2000 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. T1 - Noncommutative analysis : main ideas, definitions, and theorems T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2000 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Savin, Anton A1 - Sternin, Boris Ju. T1 - Eta-invariant and pontrjagin duality in K-theory T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2000 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. T1 - Exactly soluble commutation relations T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2000 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. T1 - Applications of noncommutative analysis to operator algebras on singular manifolds T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2000 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Nazajkinskij, Vladimir E. A1 - Sternin, Boris Ju. A1 - Schulze, Bert-Wolfgang T1 - The index of quantized contact transformations on manifolds with conical singularities Y1 - 1999 SN - 0002-3264 SN - 0869-5652 ER - TY - JOUR A1 - Nazajkinskij, Vladimir E. A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - Quantizational of canonical transformations on manifolds with conical singularities Y1 - 1999 SN - 0002-3264 SN - 0869-5652 ER - TY - JOUR A1 - Nazajkinskij, Vladimir E. A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - The Atiyah-Bott-Lefschetz formula for elliptic operators on manifolds with conical singularities Y1 - 1999 SN - 0002-3264 SN - 0869-5652 ER - TY - JOUR A1 - Nazajkinskij, Vladimir E. A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - Spectral boundary value problems and elliptic equations on manifolds with singularities Y1 - 1999 SN - 0002-3264 SN - 0869-5652 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - On boundary value problems for elliptic equations Y1 - 1999 SN - 0002-3264 SN - 0869-5652 ER - TY - JOUR A1 - Nazajkinskij, Vladimir E. A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - The Atiyah-Bott-Lefschetz theorem on manifolds with conical singularities Y1 - 1999 ER - TY - JOUR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. A1 - Satalov, Viktor E. T1 - On the index of elliptic operators on manifolds with conical singularities Y1 - 1999 SN - 0002-3264 SN - 0869-5652 ER - TY - BOOK A1 - Savin, Anton A1 - Sternin, Boris Ju. T1 - Elliptic operators in even subspaces T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 1999 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Savin, Anton A1 - Sternin, Boris Ju. T1 - Elliptic operators in odd subspaces T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 1999 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. T1 - Quantization and the wave packet transform T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 1999 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Nazajkinskij, Vladimir E. A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. T1 - Quantization of Lagrangian modules T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 1999 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Schulze, Bert-Wolfgang A1 - Nazajkinskij, Vladimir E. A1 - Sternin, Boris Ju. T1 - On the homotopy classification of elliptic operators on manifolds with singularities T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 1999 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Schulze, Bert-Wolfgang A1 - Savin, Anton A1 - Sternin, Boris Ju. T1 - The homotopy classification and the index of boundary value problems for general elliptic operators T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 1999 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - JOUR A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris Ju. T1 - On the invariant index formulas for spectral boundary value problems Y1 - 1999 ER - TY - INPR A1 - Savin, Anton A1 - Sternin, Boris T1 - Pseudodifferential subspaces and their applications in elliptic theory N2 - 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. T3 - Preprint - (2005) 17 KW - elliptic operator KW - boundary value problem KW - pseudodifferential subspace KW - dimension functional KW - η-invariant KW - index KW - modn-index KW - parity condition Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29937 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Localization problem in index theory of elliptic operators N2 - This is a survey of recent results concerning the general index locality principle, associated surgery, and their applications to elliptic operators on smooth manifolds and manifolds with singularities as well as boundary value problems. The full version of the paper is submitted for publication in Russian Mathematical Surveys. T3 - Preprint - (2001) 34 KW - elliptic operators KW - index theory KW - surgery KW - relative index KW - manifold with singularities Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26175 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Elliptic theory on manifolds with nonisolated singularities : V. Index formulas for elliptic problems on manifolds with edges N2 - For elliptic problems on manifolds with edges, we construct index formulas in form of a sum of homotopy invariant contributions of the strata (the interior of the manifold and the edge). Both terms are the indices of elliptic operators, one of which acts in spaces of sections of finite-dimensional vector bundles on a compact closed manifold and the other in spaces of sections of infinite-dimensional vector bundles over the edge. T3 - Preprint - (2003) 02 KW - manifold with edge KW - elliptic problem KW - index formula KW - symmetry conditions Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26500 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Differential operators on manifolds with singularities : analysis and topology : Chapter 1: Localization (surgery) in elliptic theory N2 - Contents: Chapter 1: Localization (Surgery) in Elliptic Theory 1.1. The Index Locality Principle 1.1.1. What is locality? 1.1.2. A pilot example 1.1.3. Collar spaces 1.1.4. Elliptic operators 1.1.5. Surgery and the relative index theorem 1.2. Surgery in Index Theory on Smooth Manifolds 1.2.1. The Booß–Wojciechowski theorem 1.2.2. The Gromov–Lawson theorem 1.3. Surgery for Boundary Value Problems 1.3.1. Notation 1.3.2. General boundary value problems 1.3.3. A model boundary value problem on a cylinder 1.3.4. The Agranovich–Dynin theorem 1.3.5. The Agranovich theorem 1.3.6. Bojarski’s theorem and its generalizations 1.4. (Micro)localization in Lefschetz theory 1.4.1. The Lefschetz number 1.4.2. Localization and the contributions of singular points 1.4.3. The semiclassical method and microlocalization 1.4.4. The classical Atiyah–Bott–Lefschetz theorem T3 - Preprint - (2003) 06 Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26546 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Elliptic theory on manifolds with nonisolated singularities : III. The spectral flow of families of conormal symbols N2 - When studyind elliptic operators on manifolds with nonisolated singularities one naturally encounters families of conormal symbols (i.e. operators elliptic with parameter p ∈ IR in the sense of Agranovich-Vishik) parametrized by the set of singular points. For homotopies of such families we define the notion of spectral flow, which in this case is an element of the K-group of the parameter space. We prove that the spectral flow is equal to the index of some family of operators on the infinite cone. T3 - Preprint - (2002) 20 KW - elliptic family KW - conormal symbol KW - spectral flow KW - relative index Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26386 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Elliptic theory on manifolds with nonisolated singularities : IV. Obstructions to elliptic problems on manifolds with edges N2 - The obstruction to the existence of Fredholm problems for elliptic differentail operators on manifolds with edges is a topological invariant of the operator. We give an explicit general formula for this invariant. As an application we compute this obstruction for geometric operators. T3 - Preprint - (2002) 24 KW - manifolds with edges KW - edge-degenerate operators KW - elliptic families KW - edge symbol KW - Atiyah-Bott obstruction KW - parameter-dependent ellipticity Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26415 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Savin, Anton A1 - Sternin, Boris T1 - Elliptic operators in subspaces and the eta invariant N2 - The paper deals with the calculation of the fractional part of the η-invariant for elliptic self-adjoint operators in topological terms. The method used to obtain the corresponding formula is based on the index theorem for elliptic operators in subspaces obtained in [1], [2]. It also utilizes K-theory with coefficients Zsub(n). In particular, it is shown that the group K(T*M,Zsub(n)) is realized by elliptic operators (symbols) acting in appropriate subspaces. T3 - Preprint - (1999) 14 KW - index of elliptic operators in subspaces KW - K-theory KW - eta-invariant KW - mod k index KW - Atiyah-Patodi-Singer theory Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25496 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris A1 - Savin, Anton T1 - The homotopy classification and the index of boundary value problems for general elliptic operators N2 - We give the homotopy classification and compute the index of boundary value problems for elliptic equations. The classical case of operators that satisfy the Atiyah-Bott condition is studied first. We also consider the general case of boundary value problems for operators that do not necessarily satisfy the Atiyah-Bott condition. T3 - Preprint - (1999) 20 KW - elliptic boundary value problems KW - Atiyah-Bott condition KW - index theory KW - K-theory KW - homotopy classification Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25568 ER - 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 - Savin, Anton A1 - Sternin, Boris T1 - Elliptic operators in odd subspaces N2 - An elliptic theory is constructed for operators acting in subspaces defined via even pseudodifferential projections. Index formulas are obtained for operators on compact manifolds without boundary and for general boundary value problems. A connection with Gilkey's theory of η-invariants is established. T3 - Preprint - (1999) 11 KW - index of elliptic operators in subspaces KW - K-theory KW - eta invariant KW - Atiyah-Patodi-Singer theory KW - boundary value problems Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25478 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 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Quantization methods in differential equations : Chapter 11: Noncommutative analysis and high-frequency asymptotics N2 - Content: Chapter 11: Noncommutative Analysis and High-Frequency Asymptotics 11.1 Statement of the Problem 11.2 Mixed Asymptotics: the General Scheme 11.3 The Asymptotic Solution of Main Problem 11.4 Analysis of the Asymptotic Solution T3 - Preprint - (2000) 20 Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25857 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 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Elliptic theory on manifolds with nonisolated singularities : I. The index of families of cone-degenerate operators N2 - We study the index problem for families of elliptic operators on manifolds with conical singularities. The relative index theorem concerning changes of the weight line is obtained. AN index theorem for families whose conormal symbols satisfy some symmetry conditions is derived. T3 - Preprint - (2002) 14 KW - elliptic family KW - conormal symbol KW - relative index KW - index formulas KW - symmetry conditions Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26327 ER - TY - INPR A1 - Nazaikinskii, Vladimir A1 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Elliptic theory on manifolds with nonisolated singularities : II. Products in elliptic theory on manifolds with edges N2 - Exterior tensor products of elliptic operators on smooth manifolds and manifolds with conical singularities are used to obtain examples of elliptic operators on manifolds with edges that do not admit well-posed edge boundary and coboundary conditions. T3 - Preprint - (2002) 15 KW - exterior tensor product KW - edge-degenerate operators KW - elliptic families KW - conormal symbol KW - Atiyah-Bott obstruction Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26335 ER - TY - INPR A1 - Savin, Anton A1 - Sternin, Boris T1 - Eta invariant and parity conditions N2 - We give a formula for the η-invariant of odd order operators on even-dimensional manifolds, and for even order operators on odd-dimensional manifolds. Geometric second order operators are found with nontrivial η-invariants. This solves a problem posed by P. Gilkey. T3 - Preprint - (2000) 21 KW - eta invariant KW - parity conditions KW - K-theory KW - linking coefficients KW - Dirac operators KW - spectral flow KW - elliptic operators Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25869 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 - Savin, Anton A1 - Schulze, Bert-Wolfgang A1 - Sternin, Boris T1 - Elliptic operators in subspaces N2 - We construct elliptic theory in the subspaces, determined by pseudodifferential projections. The finiteness theorem as well as index formula are obtained for elliptic operators acting in the subspaces. Topological (K-theoretic) aspects of the theory are studied in detail. T3 - Preprint - (2000) 04 KW - pseudodifferential subspaces KW - elliptic operators in subspaces KW - Fredholm property KW - index KW - K-theory KW - problem of classification Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25701 ER -