Heat Kernels And Spectral Theory
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Heat Kernels And Spectral Theory
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Author : E. B. Davies
language : en
Publisher: Cambridge University Press
Release Date : 1989
Heat Kernels And Spectral Theory written by E. B. 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 1989 with Mathematics categories.
Heat Kernels and Spectral Theory investigates the theory of second-order elliptic operators.
The Heat Kernel And Theta Inversion On Sl2 C
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Author : Jay Jorgenson
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-20
The Heat Kernel And Theta Inversion On Sl2 C written by Jay Jorgenson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-20 with Mathematics categories.
The worthy purpose of this text is to provide a complete, self-contained development of the trace formula and theta inversion formula for SL(2,Z[i])\SL(2,C). Unlike other treatments of the theory, the approach taken here is to begin with the heat kernel on SL(2,C) associated to the invariant Laplacian, which is derived using spherical inversion. The heat kernel on the quotient space SL(2,Z[i])\SL(2,C) is arrived at through periodization, and further expanded in an eigenfunction expansion. A theta inversion formula is obtained by studying the trace of the heat kernel. Following the author's previous work, the inversion formula then leads to zeta functions through the Gauss transform./
Spectral Theory And Differential Operators
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Author : E. Brian Davies
language : en
Publisher: Cambridge University Press
Release Date : 1995
Spectral Theory And Differential Operators 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 1995 with Mathematics categories.
This book could be used either for self-study or as a course text, and aims to lead the reader to the more advanced literature on partial differential operators.
Mathematical Physics Spectral Theory And Stochastic Analysis
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Author : Michael Demuth
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-07-08
Mathematical Physics Spectral Theory And Stochastic Analysis written by Michael Demuth and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-08 with Mathematics categories.
This volume presents self-contained survey articles on modern research areas written by experts in their fields. The topics are located at the interface of spectral theory, theory of partial differential operators, stochastic analysis, and mathematical physics. The articles are accessible to graduate students and researches from other fields of mathematics or physics while also being of value to experts, as they report on the state of the art in the respective fields.
Heat Kernel And Analysis On Manifolds
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Author : Alexander Grigor'yan
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Heat Kernel And Analysis On Manifolds written by Alexander Grigor'yan 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 2009 with Gaussian processes categories.
The heat kernel has long been an essential tool in both classical and modern mathematics but has become especially important in geometric analysis as a result of major innovations beginning in the 1970s. The methods based on heat kernels have been used in areas as diverse as analysis, geometry, and probability, as well as in physics. This book is a comprehensive introduction to heat kernel techniques in the setting of Riemannian manifolds, which inevitably involves analysis of the Laplace-Beltrami operator and the associated heat equation. The first ten chapters cover the foundations of the subject, while later chapters deal with more advanced results involving the heat kernel in a variety of settings. The exposition starts with an elementary introduction to Riemannian geometry, proceeds with a thorough study of the spectral-theoretic, Markovian, and smoothness properties of the Laplace and heat equations on Riemannian manifolds, and concludes with Gaussian estimates of heat kernels. Grigor'yan has written this book with the student in mind, in particular by including over 400 exercises. The text will serve as a bridge between basic results and current research.Titles in this series are co-published with International Press, Cambridge, MA, USA.
Spectral Graph Theory
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Author : Fan R. K. Chung
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Spectral Graph Theory written by Fan R. K. Chung 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 1997 with Eigenvalues categories.
This text discusses spectral graph theory.
Heat Kernels And Dirac Operators
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Author : Nicole Berline
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-12-08
Heat Kernels And Dirac Operators written by Nicole Berline and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-08 with Mathematics categories.
In the first edition of this book, simple proofs of the Atiyah-Singer Index Theorem for Dirac operators on compact Riemannian manifolds and its generalizations (due to the authors and J.-M. Bismut) were presented, using an explicit geometric construction of the heat kernel of a generalized Dirac operator; the new edition makes this popular book available to students and researchers in an attractive paperback.
Operator Calculus And Spectral Theory
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Author : M. Demuth
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Operator Calculus And Spectral Theory written by M. Demuth 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 Science categories.
Functional Inequalities Markov Semigroups And Spectral Theory
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Author : Fengyu Wang
language : en
Publisher: Elsevier
Release Date : 2006-04-06
Functional Inequalities Markov Semigroups And Spectral Theory written by Fengyu Wang and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-06 with Mathematics categories.
In this book, the functional inequalities are introduced to describe:(i) the spectrum of the generator: the essential and discrete spectrums, high order eigenvalues, the principle eigenvalue, and the spectral gap;(ii) the semigroup properties: the uniform intergrability, the compactness, the convergence rate, and the existence of density;(iii) the reference measure and the intrinsic metric: the concentration, the isoperimetic inequality, and the transportation cost inequality.
Heat Kernels And Analysis On Manifolds Graphs And Metric Spaces
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Author : Pascal Auscher
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Heat Kernels And Analysis On Manifolds Graphs And Metric Spaces written by Pascal Auscher 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 2003 with Mathematics categories.
This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincare Institute (Paris). In the book, leading experts introduce recent research in their fields. The unifying theme is the study of heat kernels in various situations using related geometric and analytic tools. Topics include analysis of complex-coefficient elliptic operators, diffusions on fractals and on infinite-dimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolev-type spaces on metric spaces, quasi-regular mappings and $p$-Laplace operators, heat kernel and spherical inversion on $SL 2(C)$, random walks and spectral geometry on crystal lattices, isoperimetric and isocapacitary inequalities, and generating function techniques for random walks on graphs. This volume is suitable for graduate students and research mathematicians interested in random processes and analysis on manifolds.