Boundary value problems, Schrödinger operators, deformation quantization:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin
Akad.-Verl.
1995
|
| Edition: | 1. ed. |
| Series: | Mathematical topics
8 : Advances in partial differential equations |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | 353 S. |
| ISBN: | 3055016998 |
Staff View
MARC
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| 245 | 1 | 0 | |a Boundary value problems, Schrödinger operators, deformation quantization |c ed. by Michael Demuth ... |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Berlin |b Akad.-Verl. |c 1995 | |
| 300 | |a 353 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Mathematical topics |v 8 : Advances in partial differential equations | |
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| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Boundary value problems | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
The Variable Discrete Asymptotics in Pseudo-Differential Boundary
Value Problems II 9
B.-W. Schulze
Introduction 10
6 Green Operators 10
7 Smoothing Mellin Operators 19
8 Pseudo-Differential Boundary Value Problems 29
9 Ellipticity and Regularity of Solutions with Variable Discrete Asymp¬
totics 35
10 Appendix: The Composition Rules on Symbolic and Operator Level . 47
References 67
Boundary Value Problems in Boutet de Monvel s Algebra for Manifolds
with Conical Singularities II 70
E. Schrohe and B.-W. Schulze
Introduction 71
1 Review of Smoothing Mellin and Green Operators 74
1.1 Notation. Manifolds with Conical Singularities 74
1.2 Symbols and Sobolev Spaces 75
1.3 Boutet de Monvel s Calculus 79
1.4 Sobolev Spaces Based on the Mellin Transform 84
1.5 Spaces with Asymptotics 90
1.6 Green Operators. The Algebras CG{XA,g) and CG(ID ,g) ... 92
1.7 Mellin Symbols with Values in Boutet de Monvel s Algebra . . 95
1.8 Mellin Operators and Green Operators 99
1.9 The Algebras Cm+g(Xa,g) and Cm+g(1D ,g,) 100
Contents 7
2 The Cone Algebra without Asymptotics 103
2.1 General Mellin Symbols with Values in Boutet de Monvel s Al¬
gebra 103
2.2 The Kernels of Mellin Symbols 110
2.3 Compositions and Adjoints 125
2.4 Mellin Quantization 130
3 The Cone Algebra with Asymptotics 139
3.1 The Cone Pseudodifferential Operators 139
3.2 The Algebra Structure 166
3.3 Ellipticity, Parametrices, and the Fredholm Property 171
4 Appendix 180
4.1 A Theorem on Analytic Fredholm Families 180
4.2 The Cone Sobolev Spaces H cone 186
4.3 Spectral Invariance of Parameter-Dependent Pseudodifferential
Operators 190
4.4 B0 d(X;R ) Has an Open Group of Invertible Elements .... 195
4.5 List of Misprints for Part I 199
References 202
The Index Theorem for Deformation Quantization 206
Boris V. Fedosov
Introduction 206
1 Preliminary Material 209
1.1 A -Theory 209
Primary Definitions 209
A -Theory with Compact Supports 212
The Thorn Isomorphism 217
Fredholm Families 220
1.2 Pseudodifferential Operators 223
The Weyl Algebra and the Fock Space 223
The Bott Generator 226
2 Deformation Quantization 232
2.1 Deformation Quantum Algebras 232
2.2 The Heisenberg Equation 241
2.3 Isomorphisms of Quantum Algebras 247
2.4 A Trace on Quantum Algebras 257
3 The Index Theorem for Quantum Algebras 260
3.1 Properties of the Index 260
3.2 The Thorn Isomorphism for Quantum Algebras 265
3.3 Operator-Valued Coefficients 269
3.4 Formal Coefficients 277
8 Contents
3.5 Reordering Procedure 284
3.6 Quantum Algebras on Total Space 297
3.7 The Case of R2 303
3.8 Completion of the Proof 314
References 317
A Trace Density in Deformation Quantization 319
Boris V. Fedosov
Introduction 319
1 Existence of the Trace Density 322
2 Applications to the Index Theorem 327
References 333
The Discrete Spectrum in Gaps of the Perturbed Periodic Schrodinger
Operator I: Regular Perturbations 334
M. Sh. Birman
Introduction 334
1 Preliminary Material 335
2 Statements of the Main Results 340
3 The Proof of Theorem 2.4 345
4 The Proof of Theorem 2.8 348
References 351
List of Authors 353
|
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| discipline | Mathematik |
| edition | 1. ed. |
| format | Book |
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| genre_facet | Konferenzschrift |
| id | DE-604.BV010386856 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:51:37Z |
| institution | BVB |
| isbn | 3055016998 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006916082 |
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| owner_facet | DE-355 DE-BY-UBR DE-12 DE-29T DE-703 DE-634 DE-11 |
| physical | 353 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Akad.-Verl. |
| record_format | marc |
| series | Mathematical topics |
| series2 | Mathematical topics |
| spelling | Boundary value problems, Schrödinger operators, deformation quantization ed. by Michael Demuth ... 1. ed. Berlin Akad.-Verl. 1995 353 S. txt rdacontent n rdamedia nc rdacarrier Mathematical topics 8 : Advances in partial differential equations Literaturangaben Groupes quantiques ram Perturbation (Mathématiques) ram Problèmes aux limites ram Schrödinger, opérateur de ram Mathematische Physik Boundary value problems Mathematical physics Congresses Perturbation (Mathematics) Quantum groups Schrödinger operator Hamilton-Operator (DE-588)4072278-8 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Quantisierung Physik (DE-588)4176603-9 gnd rswk-swf Deformation Mathematik (DE-588)4011284-6 gnd rswk-swf Pseudodifferentialoperator (DE-588)4047640-6 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Deformation Mathematik (DE-588)4011284-6 s Quantisierung Physik (DE-588)4176603-9 s DE-604 Hamilton-Operator (DE-588)4072278-8 s Pseudodifferentialoperator (DE-588)4047640-6 s Randwertproblem (DE-588)4048395-2 s Demuth, Michael 1946- Sonstige (DE-588)130367478 oth Mathematical topics 8 : Advances in partial differential equations (DE-604)BV008671507 8 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006916082&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Boundary value problems, Schrödinger operators, deformation quantization Mathematical topics Groupes quantiques ram Perturbation (Mathématiques) ram Problèmes aux limites ram Schrödinger, opérateur de ram Mathematische Physik Boundary value problems Mathematical physics Congresses Perturbation (Mathematics) Quantum groups Schrödinger operator Hamilton-Operator (DE-588)4072278-8 gnd Randwertproblem (DE-588)4048395-2 gnd Quantisierung Physik (DE-588)4176603-9 gnd Deformation Mathematik (DE-588)4011284-6 gnd Pseudodifferentialoperator (DE-588)4047640-6 gnd |
| subject_GND | (DE-588)4072278-8 (DE-588)4048395-2 (DE-588)4176603-9 (DE-588)4011284-6 (DE-588)4047640-6 (DE-588)1071861417 |
| title | Boundary value problems, Schrödinger operators, deformation quantization |
| title_auth | Boundary value problems, Schrödinger operators, deformation quantization |
| title_exact_search | Boundary value problems, Schrödinger operators, deformation quantization |
| title_full | Boundary value problems, Schrödinger operators, deformation quantization ed. by Michael Demuth ... |
| title_fullStr | Boundary value problems, Schrödinger operators, deformation quantization ed. by Michael Demuth ... |
| title_full_unstemmed | Boundary value problems, Schrödinger operators, deformation quantization ed. by Michael Demuth ... |
| title_short | Boundary value problems, Schrödinger operators, deformation quantization |
| title_sort | boundary value problems schrodinger operators deformation quantization |
| topic | Groupes quantiques ram Perturbation (Mathématiques) ram Problèmes aux limites ram Schrödinger, opérateur de ram Mathematische Physik Boundary value problems Mathematical physics Congresses Perturbation (Mathematics) Quantum groups Schrödinger operator Hamilton-Operator (DE-588)4072278-8 gnd Randwertproblem (DE-588)4048395-2 gnd Quantisierung Physik (DE-588)4176603-9 gnd Deformation Mathematik (DE-588)4011284-6 gnd Pseudodifferentialoperator (DE-588)4047640-6 gnd |
| topic_facet | Groupes quantiques Perturbation (Mathématiques) Problèmes aux limites Schrödinger, opérateur de Mathematische Physik Boundary value problems Mathematical physics Congresses Perturbation (Mathematics) Quantum groups Schrödinger operator Hamilton-Operator Randwertproblem Quantisierung Physik Deformation Mathematik Pseudodifferentialoperator Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006916082&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008671507 |
| work_keys_str_mv | AT demuthmichael boundaryvalueproblemsschrodingeroperatorsdeformationquantization |