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 - Schulze, Bert-Wolfgang
A1 - Sternin, Boris
T1 - Quantization methods in differential equations : Part II: Quantization by the method of ordered operators (Noncommutative Analysis) : Chapter 1: Noncommutative Analysis: Main Ideas, Definitions, and Theorems
N2 - Content: 0.1 Preliminary Remarks Chapter 1: Noncommutative Analysis: Main Ideas, Definitions, and Theorems 1.1 Functions of One Operator (Functional Calculi) 1.2 Functions of Several Operators 1.3 Main Formulas of Operator Calculus 1.4 Main Tools of Noncommutative Analysis 1.5 Composition Laws and Ordered Representations
T3 - Preprint - (2000) 11
Y1 - 2000
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25762
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 - 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 - 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 - 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 -