L2-indices for Perturbed Dirac Operators on Odd Dimensional Open Complete Manifolds PDF Download
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Author: Cezary Gajdzinski
Publisher:
ISBN:
Category : Elliptic operators
Languages : en
Pages : 156
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Author: Cezary Gajdzinski
Publisher:
ISBN:
Category : Elliptic operators
Languages : en
Pages : 156
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Author: Paul Kirk
Publisher: American Mathematical Soc.
ISBN: 082180538X
Category : Mathematics
Languages : en
Pages : 73
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Book Description
The analytic perturbation theory for eigenvalues of Dirac operators on odd dimensional manifolds with boundary is described in terms of [italic]extended L2 eigenvectors [end italics] on manifolds with cylindrical ends. These are generalizations of the Atiyah-Patodi-Singer extended [italic capital]L2 kernel of a Dirac operator. We prove that they form a discrete set near zero and deform analytically, in contrast to [italic capital]L2 eigenvectors, which can be absorbed into the continuous spectrum under deformations when the tangential operator is not invertible. We show that the analytic deformation theory for extended [italic capital]L2 eigenvectors and Atiyah-Patodi-Singer eigenvectors coincides.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 966
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Author: Nicolae Anghel
Publisher:
ISBN:
Category :
Languages : en
Pages : 134
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Author: Jan Cnops
Publisher: Springer Science & Business Media
ISBN: 1461200652
Category : Mathematics
Languages : en
Pages : 219
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Book Description
The chapters on Clifford algebra and differential geometry can be used as an introduction to the topics, and are suitable for senior undergraduates and graduates. The other chapters are also accessible at this level.; This self-contained book requires very little previous knowledge of the domains covered, although the reader will benefit from knowledge of complex analysis, which gives the basic example of a Dirac operator.; The more advanced reader will appreciate the fresh approach to the theory, as well as the new results on boundary value theory.; Concise, but self-contained text at the introductory grad level. Systematic exposition.; Clusters well with other Birkhäuser titles in mathematical physics.; Appendix. General Manifolds * List of Symbols * Bibliography * Index
Author: Catarina Carvalho
Publisher:
ISBN:
Category :
Languages : en
Pages :
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We give an index formula for a class of Dirac operators coupled with unbounded potentials. More precisely, we study operators of the form P := = D + V, where = D is a Dirac operators and V is an unbounded potential at infinity on a possibly noncompact manifold M0. We assume that M0 is a Lie manifold with compactification denoted M. Examples of Lie manifolds are provided by asymptotically Euclidean or asymptotically hyperbolic spaces. The potential V is required to be such that V is invertible outside a compact set K and V .1 extends to a smooth function on M rK that vanishes on all faces of M in a controlled way. Using tools from analysis on non-compact Riemannian manifolds, we show that the computation of the index of P reduces to the computation of the index of an elliptic pseudodifferential operator of order zero on M0 that is a multiplication operator at infinity. The index formula for P can then be obtained from the results of [17]. The proof also yields similar index formulas for Dirac operators coupled with bounded potentials that are invertible at infinity on asymptotically commutative Lie manifolds, a class of manifolds that includes the scattering and double-edge calculi.
Author: Levi Lopes de Lima
Publisher:
ISBN:
Category : Dirac equation
Languages : en
Pages : 136
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Author: Richard Melrose
Publisher: CRC Press
ISBN: 1439864608
Category : Mathematics
Languages : en
Pages : 392
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Book Description
Based on the lecture notes of a graduate course given at MIT, this sophisticated treatment leads to a variety of current research topics and will undoubtedly serve as a guide to further studies.
Author: Matthias Lesch
Publisher:
ISBN:
Category :
Languages : de
Pages : 14
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Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 884
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