The major goal of this book is to make the theory of elliptic boundary problems accessible to mathematicians and physicists working in global analysis and operator algebras. The book is about operators of Dirac type on manifolds with boundary....what's?
Author(s): Bernhelm Booß-Bavnbek, Krzysztof P. Wojciechhowski
Series: Mathematics: Theory & Applications
Edition: 1
Publisher: Birkhäuser Boston
Year: 1993
Language: English
Pages: 327
Front Cover......Page 1
Title......Page 4
Copyright......Page 5
Contents......Page 6
Preface......Page 8
List of Notations......Page 16
Part I. CLIFFORD ALGEBRAS AND Dirac OPERATORS ......Page 20
1. Clifford Algebras and Clifford Modules ......Page 22
2. Clifford Bundles and Compatible Connections ......Page 29
3. Dirac Operators ......Page 38
4. Dirac Laplacian and Connection Laplacian ......Page 45
5. Eudidean Examples ......Page 48
6. The Classical Dirac (Atiyah-Singer) Operators on Spin Manifolds ......Page 55
7. Dirac Operators and Chirality ......Page 59
8. Unique Continuation Property for Dirac Operators ......Page 62
9. Invertible Doubles......Page 69
10. Clueing Constructions. Relative Index Theorem ......Page 78
PART II. ANALYTICAL AND TOPOLOGICAL TOOLS......Page 84
11. Sobolev Spaces on Manifolds with Boundary ......Page 86
12. Calderon Projector for Dirac Operators ......Page 94
13. Existence of of Null Space Elements ......Page 114
14. Spectral Projections of Dirac Operators ......Page 124
15. Pseudo-Differential Grassmannians ......Page 130
A. Elementary Decompositions and Deformations ......Page 146
B. The Homotopy Groups of C. ......Page 152
A. Continuity of Eigenvalues ......Page 157
B. The Spectral Flow on Loops in F. ......Page 159
C. Spectral Flow and Index ......Page 164
D. Non-Vanishing Spectral Flow ......Page 176
Part III. APPLICATIONS......Page 180
18. Elliptic Boundary Problems and Pseudo-Differential Projections ......Page 182
19. Regularity of Solutions of Elliptic Boundary Problems ......Page 199
20. Fredhoim Property of the Operator AR ......Page 207
21. Exchanges on the Boundary: Type Formulas and the Cobordism Theorem for Dirac Operators . ......Page 224
A. Preliminary Remarks ......Page 230
B. Heat Kernels on the Cylinder ......Page 233
C. Duhamel's principle. Heat Kernels on Manifolds with Boundary ......Page 250
D. Proof of the Index Formula ......Page 258
E. L2-Reformulation ......Page 261
F. The Odd-Dimensional Case. A Three-Dimensional Example ......Page 267
23. Some R2marks on the Index of Generalized Atiyah-Patodi-Singer Problems ......Page 272
24. Bojarski's Theorem. General Linear Conjugation Problems ......Page 281
25. Cutting and Pasting of Elliptic Operators ......Page 295
26. Dirac Operators on the Two-Sphere ......Page 301
Bibliography ......Page 308
Index ......Page 322
Back Cover......Page 327
