Elliptic Boundary Problems for Dirac Operators [electronic resource] /

Elliptic Boundary Problems for Dirac Operators [electronic resource] /

Elliptic boundary problems have enjoyed interest recently, espe­ cially among C* -algebraists and mathematical physicists who want to understand single aspects of the theory, such as the behaviour of Dirac operators and their solution spaces in the case of a non-trivial boundary. However, the theory of elliptic boundary problems by far has not achieved the same status as the theory of elliptic operators on closed (compact, without boundary) manifolds. The latter is nowadays rec­ ognized by many as a mathematical work of art and a very useful technical tool with applications to a multitude of mathematical con­ texts. Therefore, the theory of elliptic operators on closed manifolds is well-known not only to a small group of specialists in partial dif­ ferential equations, but also to a broad range of researchers who have specialized in other mathematical topics. Why is the theory of elliptic boundary problems, compared to that on closed manifolds, still lagging behind in popularity? Admittedly, from an analytical point of view, it is a jigsaw puzzle which has more pieces than does the elliptic theory on closed manifolds. But that is not the only reason.

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Bibliographic Details
Main Authors: Booß-Bavnbek, Bernhelm. author., Wojciechowski, Krzysztof P. author., SpringerLink (Online service)
Format: Texto biblioteca
Language:eng
Published: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 1993
Subjects:Mathematics., Matrix theory., Algebra., Operator theory., Differential equations., Partial differential equations., Partial Differential Equations., Ordinary Differential Equations., Operator Theory., Linear and Multilinear Algebras, Matrix Theory.,
Online Access:http://dx.doi.org/10.1007/978-1-4612-0337-7
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record_format koha
institution COLPOS
collection Koha
country México
countrycode MX
component Bibliográfico
access En linea
En linea
databasecode cat-colpos
tag biblioteca
region America del Norte
libraryname Departamento de documentación y biblioteca de COLPOS
language eng
topic Mathematics.
Matrix theory.
Algebra.
Operator theory.
Differential equations.
Partial differential equations.
Mathematics.
Partial Differential Equations.
Ordinary Differential Equations.
Operator Theory.
Linear and Multilinear Algebras, Matrix Theory.
Mathematics.
Matrix theory.
Algebra.
Operator theory.
Differential equations.
Partial differential equations.
Mathematics.
Partial Differential Equations.
Ordinary Differential Equations.
Operator Theory.
Linear and Multilinear Algebras, Matrix Theory.
spellingShingle Mathematics.
Matrix theory.
Algebra.
Operator theory.
Differential equations.
Partial differential equations.
Mathematics.
Partial Differential Equations.
Ordinary Differential Equations.
Operator Theory.
Linear and Multilinear Algebras, Matrix Theory.
Mathematics.
Matrix theory.
Algebra.
Operator theory.
Differential equations.
Partial differential equations.
Mathematics.
Partial Differential Equations.
Ordinary Differential Equations.
Operator Theory.
Linear and Multilinear Algebras, Matrix Theory.
Booß-Bavnbek, Bernhelm. author.
Wojciechowski, Krzysztof P. author.
SpringerLink (Online service)
Elliptic Boundary Problems for Dirac Operators [electronic resource] /
description Elliptic boundary problems have enjoyed interest recently, espe­ cially among C* -algebraists and mathematical physicists who want to understand single aspects of the theory, such as the behaviour of Dirac operators and their solution spaces in the case of a non-trivial boundary. However, the theory of elliptic boundary problems by far has not achieved the same status as the theory of elliptic operators on closed (compact, without boundary) manifolds. The latter is nowadays rec­ ognized by many as a mathematical work of art and a very useful technical tool with applications to a multitude of mathematical con­ texts. Therefore, the theory of elliptic operators on closed manifolds is well-known not only to a small group of specialists in partial dif­ ferential equations, but also to a broad range of researchers who have specialized in other mathematical topics. Why is the theory of elliptic boundary problems, compared to that on closed manifolds, still lagging behind in popularity? Admittedly, from an analytical point of view, it is a jigsaw puzzle which has more pieces than does the elliptic theory on closed manifolds. But that is not the only reason.
format Texto
topic_facet Mathematics.
Matrix theory.
Algebra.
Operator theory.
Differential equations.
Partial differential equations.
Mathematics.
Partial Differential Equations.
Ordinary Differential Equations.
Operator Theory.
Linear and Multilinear Algebras, Matrix Theory.
author Booß-Bavnbek, Bernhelm. author.
Wojciechowski, Krzysztof P. author.
SpringerLink (Online service)
author_facet Booß-Bavnbek, Bernhelm. author.
Wojciechowski, Krzysztof P. author.
SpringerLink (Online service)
author_sort Booß-Bavnbek, Bernhelm. author.
title Elliptic Boundary Problems for Dirac Operators [electronic resource] /
title_short Elliptic Boundary Problems for Dirac Operators [electronic resource] /
title_full Elliptic Boundary Problems for Dirac Operators [electronic resource] /
title_fullStr Elliptic Boundary Problems for Dirac Operators [electronic resource] /
title_full_unstemmed Elliptic Boundary Problems for Dirac Operators [electronic resource] /
title_sort elliptic boundary problems for dirac operators [electronic resource] /
publisher Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser,
publishDate 1993
url http://dx.doi.org/10.1007/978-1-4612-0337-7
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spelling KOHA-OAI-TEST:1837592018-07-30T23:05:12ZElliptic Boundary Problems for Dirac Operators [electronic resource] / Booß-Bavnbek, Bernhelm. author. Wojciechowski, Krzysztof P. author. SpringerLink (Online service) textBoston, MA : Birkhäuser Boston : Imprint: Birkhäuser,1993.engElliptic boundary problems have enjoyed interest recently, espe­ cially among C* -algebraists and mathematical physicists who want to understand single aspects of the theory, such as the behaviour of Dirac operators and their solution spaces in the case of a non-trivial boundary. However, the theory of elliptic boundary problems by far has not achieved the same status as the theory of elliptic operators on closed (compact, without boundary) manifolds. The latter is nowadays rec­ ognized by many as a mathematical work of art and a very useful technical tool with applications to a multitude of mathematical con­ texts. Therefore, the theory of elliptic operators on closed manifolds is well-known not only to a small group of specialists in partial dif­ ferential equations, but also to a broad range of researchers who have specialized in other mathematical topics. Why is the theory of elliptic boundary problems, compared to that on closed manifolds, still lagging behind in popularity? Admittedly, from an analytical point of view, it is a jigsaw puzzle which has more pieces than does the elliptic theory on closed manifolds. But that is not the only reason.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.Elliptic boundary problems have enjoyed interest recently, espe­ cially among C* -algebraists and mathematical physicists who want to understand single aspects of the theory, such as the behaviour of Dirac operators and their solution spaces in the case of a non-trivial boundary. However, the theory of elliptic boundary problems by far has not achieved the same status as the theory of elliptic operators on closed (compact, without boundary) manifolds. The latter is nowadays rec­ ognized by many as a mathematical work of art and a very useful technical tool with applications to a multitude of mathematical con­ texts. Therefore, the theory of elliptic operators on closed manifolds is well-known not only to a small group of specialists in partial dif­ ferential equations, but also to a broad range of researchers who have specialized in other mathematical topics. Why is the theory of elliptic boundary problems, compared to that on closed manifolds, still lagging behind in popularity? Admittedly, from an analytical point of view, it is a jigsaw puzzle which has more pieces than does the elliptic theory on closed manifolds. But that is not the only reason.Mathematics.Matrix theory.Algebra.Operator theory.Differential equations.Partial differential equations.Mathematics.Partial Differential Equations.Ordinary Differential Equations.Operator Theory.Linear and Multilinear Algebras, Matrix Theory.Springer eBookshttp://dx.doi.org/10.1007/978-1-4612-0337-7URN:ISBN:9781461203377

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