Asymptotic Formulae In Spectral Geometry

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Asymptotic Formulae In Spectral Geometry

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Author : Peter B. Gilkey
language : en
Publisher: CRC Press
Release Date : 2003-12-17

Asymptotic Formulae In Spectral Geometry written by Peter B. Gilkey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-17 with Mathematics categories.

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

Spectral Geometry

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Author : Pierre H. Berard
language : en
Publisher: Springer
Release Date : 2006-11-14

Spectral Geometry written by Pierre H. Berard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Progress In Inverse Spectral Geometry

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Author : Stig I. Andersson
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Progress In Inverse Spectral Geometry written by Stig I. Andersson and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Most polynomial growth on every half-space Re (z) ::::: c. Moreover, Op(t) depends holomorphically on t for Re t> O. General references for much of the material on the derivation of spectral functions, asymptotic expansions and analytic properties of spectral functions are [A-P-S] and [Sh], especially Chapter 2. To study the spectral functions and their relation to the geometry and topology of X, one could, for example, take the natural associated parabolic problem as a starting point. That is, consider the 'heat equation': (%t + p) u(x, t) = 0 { u(x, O) = Uo(x), tP which is solved by means of the (heat) semi group V(t) = e- ; namely, u(·, t) = V(t)uoU· Assuming that V(t) is of trace class (which is guaranteed, for instance, if P has a positive principal symbol), it has a Schwartz kernel K E COO(X x X x Rt, E* ®E), locally given by 00 K(x, y; t) = L>-IAk(~k ® 'Pk)(X, y), k=O for a complete set of orthonormal eigensections 'Pk E COO(E). Taking the trace, we then obtain: 00 tA Op(t) = trace(V(t)) = 2::>- k. k=O Now, using, e. g., the Dunford calculus formula (where C is a suitable curve around a(P)) as a starting point and the standard for malism of pseudodifferential operators, one easily derives asymptotic expansions for the spectral functions, in this case for Op.

Spectral Functions In Mathematics And Physics

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Author : Klaus Kirsten
language : en
Publisher: CRC Press
Release Date : 2001-12-13

Spectral Functions In Mathematics And Physics written by Klaus Kirsten and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-12-13 with Mathematics categories.

The literature on the spectral analysis of second order elliptic differential operators contains a great deal of information on the spectral functions for explicitly known spectra. The same is not true, however, for situations where the spectra are not explicitly known. Over the last several years, the author and his colleagues have developed new,

Spectral Action In Noncommutative Geometry

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Author : Michał Eckstein
language : en
Publisher: Springer
Release Date : 2018-12-18

Spectral Action In Noncommutative Geometry written by Michał Eckstein and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-18 with Science categories.

What is spectral action, how to compute it and what are the known examples? This book offers a guided tour through the mathematical habitat of noncommutative geometry à la Connes, deliberately unveiling the answers to these questions. After a brief preface flashing the panorama of the spectral approach, a concise primer on spectral triples is given. Chapter 2 is designed to serve as a toolkit for computations. The third chapter offers an in-depth view into the subtle links between the asymptotic expansions of traces of heat operators and meromorphic extensions of the associated spectral zeta functions. Chapter 4 studies the behaviour of the spectral action under fluctuations by gauge potentials. A subjective list of open problems in the field is spelled out in the fifth Chapter. The book concludes with an appendix including some auxiliary tools from geometry and analysis, along with examples of spectral geometries. The book serves both as a compendium for researchers in the domain of noncommutative geometry and an invitation to mathematical physicists looking for new concepts.

Spectral Theory And Asymptotics Of Differential Equations

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Author :
language : en
Publisher: Elsevier
Release Date : 2011-09-21

Spectral Theory And Asymptotics Of Differential Equations written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-21 with Mathematics categories.

Spectral Theory and Asymptotics of Differential Equations

Spectral Theory And Geometry

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Author : E. Brian Davies
language : en
Publisher: Cambridge University Press
Release Date : 1999-09-30

Spectral Theory And Geometry written by E. Brian Davies and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09-30 with Mathematics categories.

Authoritative lectures from world experts on spectral theory and geometry.

Spectral Theory Of Automorphic Functions

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Author : A. B. Venkov
language : en
Publisher: American Mathematical Soc.
Release Date : 1983

Spectral Theory Of Automorphic Functions written by A. B. Venkov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.

Geometric And Arithmetic Methods In The Spectral Theory Of Multidimensional Periodic Operators

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Author : M. M. Skriganov
language : en
Publisher: American Mathematical Soc.
Release Date : 1987

Geometric And Arithmetic Methods In The Spectral Theory Of Multidimensional Periodic Operators written by M. M. Skriganov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.

Spectral Geometry

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Author : Alex Barnett
language : en
Publisher: American Mathematical Soc.
Release Date : 2012

Spectral Geometry written by Alex Barnett and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

This volume contains the proceedings of the International Conference on Spectral Geometry, held July 19-23, 2010, at Dartmouth College, Dartmouth, New Hampshire. Eigenvalue problems involving the Laplace operator on manifolds have proven to be a consistently fertile area of geometric analysis with deep connections to number theory, physics, and applied mathematics. Key questions include the measures to which eigenfunctions of the Laplacian on a Riemannian manifold condense in the limit of large eigenvalue, and the extent to which the eigenvalues and eigenfunctions of a manifold encode its geometry. In this volume, research and expository articles, including those of the plenary speakers Peter Sarnak and Victor Guillemin, address the flurry of recent progress in such areas as quantum unique ergodicity, isospectrality, semiclassical measures, the geometry of nodal lines of eigenfunctions, methods of numerical computation, and spectra of quantum graphs. This volume also contains mini-courses on spectral theory for hyperbolic surfaces, semiclassical analysis, and orbifold spectral geometry that prepared the participants, especially graduate students and young researchers, for conference lectures.