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Elliptic Boundary Problems for Dirac Operators

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Editorial Reviews

The text is divided into three parts. The first gives a detailed exposition of Dirac operators acting on sections of bundles of Clifford modules. The second presents some basic analytical and topological tools that enable the reader to analyze the nature of the index of elliptic boundary problems. Part three gives the basic theory of elliptic boundary problems and other applications of the machinery developed earlier in the book. Annotation c. Book News, Inc., Portland, OR (
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Product Details

Table of Contents

List of Notations
Pt. 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
Pt. II Analytical and Topological Tools
11 Sobolev Spaces on Manifolds with Boundary 67
12 Caldron 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 127
17 The Spectral Flow of Families of Self-Adjoint Operators 138
Pt. III Applications
18 Elliptic Boundary Problems and Pseudo-Differential Projections 163
19 Regularity of Solutions of Elliptic Boundary Problems 180
20 Fredholm Property of the Operator A[subscript R] 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 211
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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