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Author : E. B. Davies
Publisher : Cambridge University Press
Page : 212 pages
File Size : 45,66 MB
Release : 1989
Category : Mathematics
ISBN : 9780521409971
Heat Kernels and Spectral Theory investigates the theory of second-order elliptic operators.
Author : Narinder Singh Claire
Publisher :
Page : pages
File Size : 23,25 MB
Release : 2000
Category :
ISBN :
Author : Alexander Grigoryan
Publisher : American Mathematical Soc.
Page : 504 pages
File Size : 15,55 MB
Release : 2009
Category : Education
ISBN : 0821893939
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.
Author : Nicole Berline
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 12,99 MB
Release : 2003-12-08
Category : Mathematics
ISBN : 9783540200628
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.
Author : E. Brian Davies
Publisher : Cambridge University Press
Page : 198 pages
File Size : 29,11 MB
Release : 1995
Category : Mathematics
ISBN : 9780521587105
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.
Author : Fan R. K. Chung
Publisher : American Mathematical Soc.
Page : 228 pages
File Size : 20,55 MB
Release : 1997
Category : Mathematics
ISBN : 0821803158
This text discusses spectral graph theory.
Author : Michael Demuth
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 41,2 MB
Release : 2014-07-08
Category : Mathematics
ISBN : 3034805918
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.
Author : E. Brian Davies
Publisher : Cambridge University Press
Page : 344 pages
File Size : 15,34 MB
Release : 1999-09-30
Category : Mathematics
ISBN : 0521777496
Authoritative lectures from world experts on spectral theory and geometry.
Author : Jay Jorgenson
Publisher : American Mathematical Soc.
Page : 410 pages
File Size : 28,1 MB
Release : 2006
Category : Mathematics
ISBN : 0821836986
The aim of this volume is to bring together research ideas from various fields of mathematics which utilize the heat kernel or heat kernel techniques in their research. The intention of this collection of papers is to broaden productive communication across mathematical sub-disciplines and to provide a vehicle which would allow experts in one field to initiate research with individuals in another field, as well as to give non-experts a resource which can facilitate expanding theirresearch and connecting with others.
Author : Michael Demuth
Publisher : Birkhäuser
Page : 476 pages
File Size : 11,3 MB
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 3034884605
In this book, a beautiful interplay between probability theory (Markov processes, martingale theory) on the one hand and operator and spectral theory on the other yields a uniform treatment of several kinds of Hamiltonians such as the Laplace operator, relativistic Hamiltonian, Laplace-Beltrami operator, and generators of Ornstein-Uhlenbeck processes. The unified approach provides a new viewpoint of and a deeper insight into the subject.