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.

Heat Kernel And Analysis On Manifolds

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Author : Alexander Grigoryan
language : en
Publisher: American Mathematical Soc.
Release Date : 2009

Heat Kernel And Analysis On Manifolds written by Alexander Grigoryan 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 Education 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.

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.

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 Mathematics categories.

This text discusses spectral graph theory.

The Ubiquitous Heat Kernel

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Author : Jay Jorgenson
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

The Ubiquitous Heat Kernel written by Jay Jorgenson 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 2006 with Mathematics categories.

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.

Operators Geometry And Quanta

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Author : Dmitri Fursaev
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-25

Operators Geometry And Quanta written by Dmitri Fursaev 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 2011-06-25 with Science categories.

This book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum field theory. All methods are illustrated with applications to specific physical problems from the forefront of current research, such as finite-temperature field theory, D-branes, quantum solitons and noncommutativity. In the first part of the book, necessary background information on differential geometry and quantization, including less standard material, is collected. The second part of the book contains a detailed description of main spectral functions and methods of their calculation. In the third part, the theory is applied to several examples (D-branes, quantum solitons, anomalies, noncommutativity). This book addresses advanced graduate students and researchers in mathematical physics with basic knowledge of quantum field theory and differential geometry. The aim is to prepare readers to use spectral functions in their own research, in particular in relation to heat kernels and zeta functions.

Mathematics Unlimited 2001 And Beyond

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Author : Björn Engquist
language : en
Publisher: Springer
Release Date : 2017-04-05

Mathematics Unlimited 2001 And Beyond written by Björn Engquist and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-05 with Mathematics categories.

This is a book guaranteed to delight the reader. It not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future de- velopment as we enter a new millennium. True to its title, the book extends beyond the spectrum of mathematics to in- clude contributions from other related sciences. You will enjoy reading the many stimulating contributions and gain insights into the astounding progress of mathematics and the perspectives for its future. One of the editors, Björn Eng- quist, is a world-renowned researcher in computational sci- ence and engineering. The second editor, Wilfried Schmid, is a distinguished mathematician at Harvard University. Likewi- se the authors are all foremost mathematicians and scien- tists, and their biographies and photographs appear at the end of the book. Unique in both form and content, this is a "must-read" for every mathematician and scientist and, in particular, for graduates still choosing their specialty.

Analysis Of Heat Equations On Domains Lms 31

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Author : El-Maati Ouhabaz
language : en
Publisher: Princeton University Press
Release Date : 2009-01-10

Analysis Of Heat Equations On Domains Lms 31 written by El-Maati Ouhabaz and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-10 with Mathematics categories.

This is the first comprehensive reference published on heat equations associated with non self-adjoint uniformly elliptic operators. The author provides introductory materials for those unfamiliar with the underlying mathematics and background needed to understand the properties of heat equations. He then treats Lp properties of solutions to a wide class of heat equations that have been developed over the last fifteen years. These primarily concern the interplay of heat equations in functional analysis, spectral theory and mathematical physics. This book addresses new developments and applications of Gaussian upper bounds to spectral theory. In particular, it shows how such bounds can be used in order to prove Lp estimates for heat, Schrödinger, and wave type equations. A significant part of the results have been proved during the last decade. The book will appeal to researchers in applied mathematics and functional analysis, and to graduate students who require an introductory text to sesquilinear form techniques, semigroups generated by second order elliptic operators in divergence form, heat kernel bounds, and their applications. It will also be of value to mathematical physicists. The author supplies readers with several references for the few standard results that are stated without proofs.

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.

Invariance Theory

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Author : Peter B. Gilkey
language : en
Publisher: CRC Press
Release Date : 1994-12-22

Invariance Theory 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 1994-12-22 with Mathematics categories.

This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas, the Gauss-Bonnet theorem for a manifold with smooth boundary, and the geometrical theorem for a manifold with smooth boundary. The author uses invariance theory to identify the integrand of the index theorem for classical elliptic complexes with the invariants of the heat equation.