Download or read book Heat Kernels and Spectral Theory written by E. B. Davies and published by Cambridge University Press. This book was released on 1989 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Heat Kernels and Spectral Theory investigates the theory of second-order elliptic operators.
Download or read book Heat Kernel and Analysis on Manifolds written by Alexander Grigor'yan and published by American Mathematical Soc.. This book was released on 2009 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Heat Kernels and Dirac Operators written by Nicole Berline and published by Springer Science & Business Media. This book was released on 2003-12-08 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spectral Graph Theory written by Fan R. K. Chung and published by American Mathematical Soc.. This book was released on 1997 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text discusses spectral graph theory.
Download or read book Spectral Theory and Differential Operators written by E. Brian Davies and published by Cambridge University Press. This book was released on 1995 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Random Walks and Heat Kernels on Graphs written by M. T. Barlow and published by Cambridge University Press. This book was released on 2017-02-23 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Useful but hard-to-find results enrich this introduction to the analytic study of random walks on infinite graphs.
Download or read book Mathematical Physics Spectral Theory and Stochastic Analysis written by Michael Demuth and published by Springer Science & Business Media. This book was released on 2014-07-08 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Ubiquitous Heat Kernel written by Jay Jorgenson and published by American Mathematical Soc.. This book was released on 2006 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Analysis of Heat Equations on Domains LMS 31 written by El-Maati Ouhabaz and published by Princeton University Press. This book was released on 2009-01-10 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematics Unlimited 2001 and Beyond written by Björn Engquist and published by Springer. This book was released on 2017-04-05 with total page 1219 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Limited collector's edition - an exclusive and timeless work. This special, numbered edition will be available until June 1, 2000. Firm orders only.
Download or read book The Heat Kernel and Theta Inversion on SL2 C written by Jay Jorgenson and published by Springer Science & Business Media. This book was released on 2009-02-20 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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./
Download or read book Invariance Theory written by Peter B. Gilkey and published by CRC Press. This book was released on 1994-12-22 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Operators Geometry and Quanta written by Dmitri Fursaev and published by Springer Science & Business Media. This book was released on 2011-06-25 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Tauberian Theorem written by F. J. Bureau and published by . This book was released on 1960 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Operator Calculus and Spectral Theory written by M. Demuth and published by Birkhäuser. This book was released on 2012-12-06 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Functional Inequalities Markov Semigroups and Spectral Theory written by Fengyu Wang and published by Elsevier. This book was released on 2006-04-06 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Laplacian on a Riemannian Manifold written by Steven Rosenberg and published by Cambridge University Press. This book was released on 1997-01-09 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.
