Elliptic Boundary Problems for Dirac Operators

Paperback (Softcover reprint of the original 1st ed. 1993)
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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 (booknews.com)
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Product Details

  • ISBN-13: 9781461267133
  • Publisher: Birkhauser Verlag
  • Publication date: 4/30/2013
  • Series: Mathematics: Theory and Applications Series
  • Edition description: Softcover reprint of the original 1st ed. 1993
  • Edition number: 1
  • Pages: 307
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.69 (d)

Table of Contents

I. Clifford Algebras and Dirac Operators.- 1. Clifford Algebras and Clifford Modules.- 2. Clifford Bundles and Compatible Connections.- 3. Dirac Operators.- 4. Dirac Laplacian and Connection Laplacian.- 5. Euclidean Examples.- 6. The Classical Dirac (Atiyah-Singer) Operators on Spin Manifolds.- 7. Dirac Operators and Chirality.- 8. Unique Continuation Property for Dirac Operators.- 9. Invertible Doubles.- 10. Glueing Constructions. Relative Index Theorem.- II. Analytical and Topological Tools.- 11. Sobolev Spaces on Manifolds with Boundary.- 12. Calderón Projector for Dirac Operators.- 13. Existence of Traces of Null Space Elements.- 14. Spectral Projections of Dirac Operators.- 15. Pseudo-Differential Grassmannians.- 16. The Homotopy Groups of the Space of Self-Adjoint Fredholm Operators.- 17. The Spectral Flow of Families of Self-Adjoint Operators.- III. Applications.- 18. Elliptic Boundary Problems and Pseudo-Differential Projections.- 19. Regularity of Solutions of Elliptic Boundary Problems.- 20. Fredholm Property of the Operator AR.- 21. Exchanges on the Boundary: Agranovi?-Dynin Type Formulas and the Cobordism Theorem for Dirac Operators.- 22. The Index Theorem for Atiyah-Patodi-Singer Problems.- 23. Some Remarks on the Index of Generalized Atiyah-Patodi-Singer Problems.- 24. Bojarski’s Theorem. General Linear Conjugation Problems.- 25. Cutting and Pasting of Elliptic Operators.- 26. Dirac Operators on the Two-Sphere.

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