Heat Kernels And Dirac Operators
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Author | : Nicole Berline |
Publisher | : Springer Science & Business Media |
Total Pages | : 384 |
Release | : 2003-12-08 |
Genre | : Mathematics |
ISBN | : 9783540200628 |
Download Heat Kernels and Dirac Operators Book in PDF, Epub and Kindle
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 | : J.J. Duistermaat |
Publisher | : Springer Science & Business Media |
Total Pages | : 245 |
Release | : 2013-12-01 |
Genre | : Mathematics |
ISBN | : 1461253446 |
Download The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator Book in PDF, Epub and Kindle
When visiting M.I.T. for two weeks in October 1994, Victor Guillemin made me enthusiastic about a problem in symplectic geometry which involved the use of the so-called spin-c Dirac operator. Back in Berkeley, where I had l spent a sabbatical semester , I tried to understand the basic facts about this operator: its definition, the main theorems about it, and their proofs. This book is an outgrowth of the notes in which I worked this out. For me this was a great learning experience because of the many beautiful mathematical structures which are involved. I thank the Editorial Board of Birkhauser, especially Haim Brezis, for sug gesting the publication of these notes as a book. I am also very grateful for the suggestions by the referees, which have led to substantial improvements in the presentation. Finally I would like to express special thanks to Ann Kostant for her help and her prodding me, in her charming way, into the right direction. J.J. Duistermaat Utrecht, October 16, 1995.
Author | : Rafe Mazzeo |
Publisher | : |
Total Pages | : |
Release | : 1997 |
Genre | : |
ISBN | : |
Download Dirac Operators, Heat Kernels and Micrrorlocal Analysis Book in PDF, Epub and Kindle
Author | : Ovidiu Calin |
Publisher | : Springer Science & Business Media |
Total Pages | : 444 |
Release | : 2010-10-10 |
Genre | : Mathematics |
ISBN | : 0817649956 |
Download Heat Kernels for Elliptic and Sub-elliptic Operators Book in PDF, Epub and Kindle
This monograph is a unified presentation of several theories of finding explicit formulas for heat kernels for both elliptic and sub-elliptic operators. These kernels are important in the theory of parabolic operators because they describe the distribution of heat on a given manifold as well as evolution phenomena and diffusion processes. Heat Kernels for Elliptic and Sub-elliptic Operators is an ideal reference for graduate students, researchers in pure and applied mathematics, and theoretical physicists interested in understanding different ways of approaching evolution operators.
Author | : Johannes Jisse Duistermaat |
Publisher | : |
Total Pages | : 247 |
Release | : 1996 |
Genre | : Almost complex manifolds |
ISBN | : 9783764338657 |
Download The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator Book in PDF, Epub and Kindle
Author | : Alexander Grigoryan |
Publisher | : American Mathematical Soc. |
Total Pages | : 504 |
Release | : 2009 |
Genre | : Education |
ISBN | : 0821893939 |
Download Heat Kernel and Analysis on Manifolds Book in PDF, Epub and Kindle
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 | : |
Publisher | : |
Total Pages | : 260 |
Release | : 2011-12-03 |
Genre | : |
ISBN | : 9780817682484 |
Download The Heat Kernel Lefschetz Fixed Point Formula for the Spin-C Dirac Operator Book in PDF, Epub and Kindle
Author | : E. B. Davies |
Publisher | : Cambridge University Press |
Total Pages | : 212 |
Release | : 1989 |
Genre | : Mathematics |
ISBN | : 9780521409971 |
Download Heat Kernels and Spectral Theory Book in PDF, Epub and Kindle
Heat Kernels and Spectral Theory investigates the theory of second-order elliptic operators.
Author | : Ivan Avramidi |
Publisher | : Birkhäuser |
Total Pages | : 402 |
Release | : 2015-11-26 |
Genre | : Mathematics |
ISBN | : 3319262661 |
Download Heat Kernel Method and its Applications Book in PDF, Epub and Kindle
The heart of the book is the development of a short-time asymptotic expansion for the heat kernel. This is explained in detail and explicit examples of some advanced calculations are given. In addition some advanced methods and extensions, including path integrals, jump diffusion and others are presented. The book consists of four parts: Analysis, Geometry, Perturbations and Applications. The first part shortly reviews of some background material and gives an introduction to PDEs. The second part is devoted to a short introduction to various aspects of differential geometry that will be needed later. The third part and heart of the book presents a systematic development of effective methods for various approximation schemes for parabolic differential equations. The last part is devoted to applications in financial mathematics, in particular, stochastic differential equations. Although this book is intended for advanced undergraduate or beginning graduate students in, it should also provide a useful reference for professional physicists, applied mathematicians as well as quantitative analysts with an interest in PDEs.
Author | : Bernhelm Booß-Bavnbek |
Publisher | : Springer Science & Business Media |
Total Pages | : 322 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461203376 |
Download Elliptic Boundary Problems for Dirac Operators Book in PDF, Epub and Kindle
Elliptic boundary problems have enjoyed interest recently, espe cially among C* -algebraists and mathematical physicists who want to understand single aspects of the theory, such as the behaviour of Dirac operators and their solution spaces in the case of a non-trivial boundary. However, the theory of elliptic boundary problems by far has not achieved the same status as the theory of elliptic operators on closed (compact, without boundary) manifolds. The latter is nowadays rec ognized by many as a mathematical work of art and a very useful technical tool with applications to a multitude of mathematical con texts. Therefore, the theory of elliptic operators on closed manifolds is well-known not only to a small group of specialists in partial dif ferential equations, but also to a broad range of researchers who have specialized in other mathematical topics. Why is the theory of elliptic boundary problems, compared to that on closed manifolds, still lagging behind in popularity? Admittedly, from an analytical point of view, it is a jigsaw puzzle which has more pieces than does the elliptic theory on closed manifolds. But that is not the only reason.