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The Ubiquitous Heat Kernel

2006 Mathematics
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Release : 2006
Genre : Mathematics
Kind : eBook
Book Rating : 986/5 ( reviews)

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Book Synopsis The Ubiquitous Heat Kernel by : Jay Jorgenson

Download or read book The Ubiquitous Heat Kernel written by Jay Jorgenson. This book was released on 2006. 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.

Heat Kernel and Analysis on Manifolds

2009 Education
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Release : 2009
Genre : Education
Kind : eBook
Book Rating : 939/5 ( reviews)

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Book Synopsis Heat Kernel and Analysis on Manifolds by : Alexander Grigoryan

Download or read book Heat Kernel and Analysis on Manifolds written by Alexander Grigoryan. This book was released on 2009. 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.

The Heat Kernel and Theta Inversion on SL2(C)

2009-02-20 Mathematics
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Release : 2009-02-20
Genre : Mathematics
Kind : eBook
Book Rating : 329/5 ( reviews)

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Book Synopsis The Heat Kernel and Theta Inversion on SL2(C) by : Jay Jorgenson

Download or read book The Heat Kernel and Theta Inversion on SL2(C) written by Jay Jorgenson. This book was released on 2009-02-20. 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./

Mathematics Unlimited - 2001 and Beyond

2017-04-05 Mathematics
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Release : 2017-04-05
Genre : Mathematics
Kind : eBook
Book Rating : 78X/5 ( reviews)

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Book Synopsis Mathematics Unlimited - 2001 and Beyond by : Björn Engquist

Download or read book Mathematics Unlimited - 2001 and Beyond written by Björn Engquist. This book was released on 2017-04-05. 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.

Quantum Field Theory I: Basics in Mathematics and Physics

2007-04-18 Science
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Release : 2007-04-18
Genre : Science
Kind : eBook
Book Rating : 64X/5 ( reviews)

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Book Synopsis Quantum Field Theory I: Basics in Mathematics and Physics by : Eberhard Zeidler

Download or read book Quantum Field Theory I: Basics in Mathematics and Physics written by Eberhard Zeidler. This book was released on 2007-04-18. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.

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