Elliptic boundary problems for Dirac operators:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston ; Basel ; Berlin
Birkhäuser
1993
|
| Series: | Mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xviii, 307 Seiten Illustrationen, Diagramme |
| ISBN: | 0817636811 3764336811 |
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MARC
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| 245 | 1 | 0 | |a Elliptic boundary problems for Dirac operators |c Bernhelm Booß-Bavnbek ; Krzysztof P. Wojciechowski |
| 264 | 1 | |a Boston ; Basel ; Berlin |b Birkhäuser |c 1993 | |
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Record in the Search Index
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| adam_text | Contents
Preface vii
List of Notations xv
Part I. Clifford Algebras and Dirac Operators
1. Clifford Algebras and Clifford Modules 3
2. Clifford Bundles and Compatible Connections 10
3. Dirac Operators 19
4. Dirac Laplacian and Connection Laplacian 26
5. Euclidean Examples 29
6. The Classical Dirac (Atiyah Singer) Operators
on Spin Manifolds 36
7. Dirac Operators and Chirality 40
8. Unique Continuation Property for Dirac Operators 43
9. Invertible Doubles 50
10. Glueing Constructions. Relative Index Theorem 59
Part II. Analytical and Topological Tools
11. Sobolev Spaces on Manifolds with Boundary 67
12. Calderon Projector for Dirac Operators 75
13. Existence of Traces of Null Space Elements 95
14. Spectral Projections of Dirac Operators 105
15. Pseudo Differential Grassmannians 111
16. The Homotopy Groups of the Space
of Self Adjoint Fredholm Operators
A. Elementary Decompositions and Deformations 127
B. The Homotopy Groups of G* 133
17. The Spectral Flow of Families of Self Adjoint Operators
A. Continuity of Eigenvalues 138
B. The Spectral Flow on Loops in £, 140
C. Spectral Flow and Index 145
D. Non Vanishing Spectral Flow 157
Part III. Applications
18. Elliptic Boundary Problems and Pseudo Differential
Projections 163
19. Regularity of Solutions of Elliptic Boundary Problems 180
vi Contents
20. Predholm Property of the Operator Ar 188
21. Exchanges on the Boundary: Agranovic Dynin Type
Formulas and the Cobordism Theorem for Dirac Operators . 205
22. The Index Theorem for Atiyah Patodi Singer Problems
A. Preliminary Remarks 211
B. Heat Kernels on the Cylinder 214
C. Duhamel s principle. Heat Kernels on Manifolds
with Boundary 231
D. Proof of the Index Formula 239
E. L2 Reformulation 242
F. The Odd Dimensional Case.
A Three Dimensional Example 248
23. Some Remarks on the Index of Generalized
Atiyah Patodi Singer Problems 253
24. Bojarski s Theorem. General Linear
Conjugation Problems 262
25. Cutting and Pasting of Elliptic Operators 276
26. Dirac Operators on the Two Sphere 282
Bibliography 289
Index 303
|
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| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:18:59Z |
| institution | BVB |
| isbn | 0817636811 3764336811 |
| language | English |
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| physical | xviii, 307 Seiten Illustrationen, Diagramme |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Mathematics |
| spelling | Booss-Bavnbek, Bernhelm 1941- Verfasser (DE-588)108280470 aut Elliptic boundary problems for Dirac operators Bernhelm Booß-Bavnbek ; Krzysztof P. Wojciechowski Boston ; Basel ; Berlin Birkhäuser 1993 xviii, 307 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Mathematics Dirac-Operator (DE-588)4150118-4 gnd rswk-swf Elliptisches Randwertproblem (DE-588)4193399-0 gnd rswk-swf Elliptisches Randwertproblem (DE-588)4193399-0 s Dirac-Operator (DE-588)4150118-4 s DE-604 Wojciechowski, Krzysztof P. 1953- Verfasser (DE-588)172559510 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005526850&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Booss-Bavnbek, Bernhelm 1941- Wojciechowski, Krzysztof P. 1953- Elliptic boundary problems for Dirac operators Dirac-Operator (DE-588)4150118-4 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd |
| subject_GND | (DE-588)4150118-4 (DE-588)4193399-0 |
| title | Elliptic boundary problems for Dirac operators |
| title_auth | Elliptic boundary problems for Dirac operators |
| title_exact_search | Elliptic boundary problems for Dirac operators |
| title_full | Elliptic boundary problems for Dirac operators Bernhelm Booß-Bavnbek ; Krzysztof P. Wojciechowski |
| title_fullStr | Elliptic boundary problems for Dirac operators Bernhelm Booß-Bavnbek ; Krzysztof P. Wojciechowski |
| title_full_unstemmed | Elliptic boundary problems for Dirac operators Bernhelm Booß-Bavnbek ; Krzysztof P. Wojciechowski |
| title_short | Elliptic boundary problems for Dirac operators |
| title_sort | elliptic boundary problems for dirac operators |
| topic | Dirac-Operator (DE-588)4150118-4 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd |
| topic_facet | Dirac-Operator Elliptisches Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005526850&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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