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Asymptotic Formulae in Spectral Geometry (Studies in Advanced Mathematics)

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Asymptotic Formulae in Spectral Geometry (Studies in Advanced Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

A great deal of progress has been made recently in the field of asymptotic formulas that arise in the theory of Dirac and Laplace type operators. These include not only the classical heat trace asymptotics and heat content asymptotics, but also the more exotic objects encountered in the context of manifolds with boundaries and imposing suitable boundary conditions. To date, however, there has been no unified discussion of these results. Asymptotic Formulae in Spectral Geometry collects these results and computations into one book. The author focuses on the functorial and special cases methods of computing asymptotic heat trace and heat content coefficients in the heat equation and introduces results derived from the Seeley Calculus and other methods. He incorporates the work of many authors into the presentation, and includes a complete bibliography that serves as a roadmap to the literature on the subject. The formulas studied here are important not only for their intrinsic interest, but also for their applications to areas such as index theory, compactness theorems for moduli spaces of isospectral metics, and zeta function regularization. Geometers, mathematical physicists, and analysts alike will undoubtedly find this book to be up to date, well organized, and broad in scope-in short, the definitive book on the subject.

Book News Annotation:

Gilkey (mathematics, U. of Oregon) compiles into a single reference the many results that have been found recently in asymptotic formulas in the theory of Dirac and Laplace type operators. He focuses on the functorial and special case methods of computing asymptotic heat trace and heat content coefficients in the heat equation, and introduces results from the Seeley calculus and other methods. The formulas he presents can be applied in such areas as index theory, compactness theorems for moduli spaces of isospectral metrics, and zeta function regularization.
Annotation 2004 Book News, Inc., Portland, OR (booknews.com)

Synopsis:

A great deal of progress has been made recently in the field of asymptotic formulas that arise in the theory of Dirac and Laplace type operators. Asymptotic Formulae in Spectral Geometry collects these results and computations into one book. Written by a leading pioneer in the field, it focuses on the functorial and special cases methods of computing asymptotic heat trace and heat content coefficients in the heat equation. It incorporates the work of many authors into the presentation, and includes a complete bibliography that serves as a roadmap to the literature on the subject. Geometers, mathematical physicists, and analysts alike will undoubtedly find this book to be the definitive book on the subject

Product Details

ISBN:
9781584883586
Author:
Gilkey, Peter B.
Publisher:
CRC Press
Author:
Gilkey, Gilkey B.
Location:
Boca Raton
Subject:
Differential Equations
Subject:
Applied
Subject:
Geometry - Differential
Subject:
Riemannian manifolds
Subject:
Spectral geometry
Subject:
Differential equations -- Asymptotic theory.
Subject:
Mathematics-Differential Geometry
Series:
Studies in Advanced Mathematics
Series Volume:
no. 6
Publication Date:
20031231
Binding:
Hardcover
Language:
English
Illustrations:
Yes
Pages:
304
Dimensions:
9.46x6.22x.84 in. 1.23 lbs.

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Related Subjects

Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » Differential Geometry

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Product details 304 pages Chapman & Hall/CRC - English 9781584883586 Reviews:
"Synopsis" by , A great deal of progress has been made recently in the field of asymptotic formulas that arise in the theory of Dirac and Laplace type operators. Asymptotic Formulae in Spectral Geometry collects these results and computations into one book. Written by a leading pioneer in the field, it focuses on the functorial and special cases methods of computing asymptotic heat trace and heat content coefficients in the heat equation. It incorporates the work of many authors into the presentation, and includes a complete bibliography that serves as a roadmap to the literature on the subject. Geometers, mathematical physicists, and analysts alike will undoubtedly find this book to be the definitive book on the subject
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