Heat Kernel Method And Its Applications
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Heat Kernel Method And Its Applications
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Author : Ivan Avramidi
language : en
Publisher: Birkhäuser
Release Date : 2015-11-26
Heat Kernel Method And Its Applications written by Ivan Avramidi and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-26 with Mathematics categories.
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.
Heat Kernel On Lie Groups And Maximally Symmetric Spaces
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Author : Ivan G. Avramidi
language : en
Publisher: Springer Nature
Release Date : 2023-05-27
Heat Kernel On Lie Groups And Maximally Symmetric Spaces written by Ivan G. Avramidi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-27 with Mathematics categories.
This monograph studies the heat kernel for the spin-tensor Laplacians on Lie groups and maximally symmetric spaces. It introduces many original ideas, methods, and tools developed by the author and provides a list of all known exact results in explicit form – and derives them – for the heat kernel on spheres and hyperbolic spaces. Part I considers the geometry of simple Lie groups and maximally symmetric spaces in detail, and Part II discusses the calculation of the heat kernel for scalar, spinor, and generic Laplacians on spheres and hyperbolic spaces in various dimensions. This text will be a valuable resource for researchers and graduate students working in various areas of mathematics – such as global analysis, spectral geometry, stochastic processes, and financial mathematics – as well in areas of mathematical and theoretical physics – including quantum field theory, quantum gravity, string theory, and statistical physics.
Laguerre Calculus And Its Applications On The Heisenberg Group
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Author : Carlos A. Berenstein
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Laguerre Calculus And Its Applications On The Heisenberg Group written by Carlos A. Berenstein 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 2001 with Mathematics categories.
For nearly two centuries, the relation between analytic functions of one complex variable, their boundary values, harmonic functions, and the theory of Fourier series has been one of the central topics of study in mathematics. The topic stands on its own, yet also provides very useful mathematical applications. This text provides a self-contained introduction to the corresponding questions in several complex variables: namely, analysis on the Heisenberg group and the study of the solutions of the boundary Cauchy-Riemann equations. In studying this material, readers are exposed to analysis in non-commutative compact and Lie groups, specifically the rotation group and the Heisenberg groups-both fundamental in the theory of group representations and physics. Introduced in a concrete setting are the main ideas of the Calderón-Zygmund-Stein school of harmonic analysis. Also considered in the book are some less conventional problems of harmonic and complex analysis, in particular, the Morera and Pompeiu problems for the Heisenberg group, which relates to questions in optics, tomography, and engineering. The book was borne of graduate courses and seminars held at the University of Maryland (College Park), the University of Toronto (ON), Georgetown University (Washington, DC), and the University of Georgia (Athens). Readers should have an advanced undergraduate understanding of Fourier analysis and complex analysis in one variable.
Brownian Motion And Its Applications To Mathematical Analysis
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Author : Krzysztof Burdzy
language : en
Publisher: Springer
Release Date : 2014-02-07
Brownian Motion And Its Applications To Mathematical Analysis written by Krzysztof Burdzy and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-07 with Mathematics categories.
These lecture notes provide an introduction to the applications of Brownian motion to analysis and more generally, connections between Brownian motion and analysis. Brownian motion is a well-suited model for a wide range of real random phenomena, from chaotic oscillations of microscopic objects, such as flower pollen in water, to stock market fluctuations. It is also a purely abstract mathematical tool which can be used to prove theorems in "deterministic" fields of mathematics. The notes include a brief review of Brownian motion and a section on probabilistic proofs of classical theorems in analysis. The bulk of the notes are devoted to recent (post-1990) applications of stochastic analysis to Neumann eigenfunctions, Neumann heat kernel and the heat equation in time-dependent domains.
Proceedings Of The Julian Schwinger Centennial Conference
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Author : Berthold-georg Englert
language : en
Publisher: World Scientific
Release Date : 2019-10-30
Proceedings Of The Julian Schwinger Centennial Conference written by Berthold-georg Englert and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-30 with Science categories.
The Julian Schwinger Centennial Conference of 2018 assembled many of Schwinger's students, colleagues, and friends to celebrate this towering figure of twentieth century physics one hundred years after his birth. This proceedings volume collects talks delivered on this occasion. They cover a wide range of topics, all related to Schwinger's rich scientific legacy — supplemented by personal recollections about Julian Schwinger, the physicist, the teacher, and the gentleman.Also included are an essay of 1985, co-authored by Schwinger but not published previously, as well as the transcripts of speeches by distinguished colleagues at the 1978 gathering when Schwinger's sixtieth birthday was celebrated.
Heat Kernel And Quantum Gravity
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Author : Ivan G. Avramidi
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-03-27
Heat Kernel And Quantum Gravity written by Ivan G. Avramidi 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 2000-03-27 with Medical categories.
This book tackles quantum gravity via the so-called background field method and its effective action functional. The author presents an explicitly covariant and effective technique to calculate the de Witt coefficients and to analyze the Schwinger-de Wit asymptotic expansion of the effective action. He also investigates the ultraviolet behaviour of higher-derivative quantum gravity. The book addresses theoretical physicists, graduate students as well as researchers, but should also be of interest to physicists working in mathematical or elementary particle physics.
Journal Of Mathematical Sciences The University Of Tokyo
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Author :
language : en
Publisher:
Release Date : 2004
Journal Of Mathematical Sciences The University Of Tokyo written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
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.
The Method Of Layer Potentials For The Heat Equation In Time Varying Domains
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Author : John L. Lewis
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
The Method Of Layer Potentials For The Heat Equation In Time Varying Domains written by John L. Lewis 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 1995 with Mathematics categories.
This memoir consists of three papers in which we develop the method of layer potentials for the heat equation in time-varying domains. In Chapter I we show certain singular integral operators on [italic]L[superscript italic]p are bounded. in Chapter II, we develop a modification of the David buildup scheme to obtain [italic]L[superscript italic]p boundedness of the double layer heat potential on the boundary of our domains. In Chapter III, we use the results of the first two chapters to show the mutual absolute continuity of parabolic measure and a certain projective Lebesgue measure.
Partial Differential Equations With Fourier Series And Boundary Value Problems
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Author : Nakhle H. Asmar
language : en
Publisher: Courier Dover Publications
Release Date : 2017-03-23
Partial Differential Equations With Fourier Series And Boundary Value Problems written by Nakhle H. Asmar and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-23 with Mathematics categories.
Rich in proofs, examples, and exercises, this widely adopted text emphasizes physics and engineering applications. The Student Solutions Manual can be downloaded free from Dover's site; instructions for obtaining the Instructor Solutions Manual is included in the book. 2004 edition, with minor revisions.