Author | Booร-Bavnbek, Bernhelm. author |
---|---|
Title | Elliptic Boundary Problems for Dirac Operators [electronic resource] / by Bernhelm Booร-Bavnbek, Krzysztof P. Wojciechowski |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1993 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0337-7 |
Descript | XVIII, 307 p. online resource |
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. Calderรณn 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. Bojarskiโs Theorem. General Linear Conjugation Problems -- 25. Cutting and Pasting of Elliptic Operators -- 26. Dirac Operators on the Two-Sphere