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Heat Kernel And Analysis On Manifolds


Heat Kernel And Analysis On Manifolds
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Heat Kernel And Analysis On Manifolds


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 Mathematics categories.


"This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincaré 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."--Publisher's website.



The Laplacian On A Riemannian Manifold


The Laplacian On A Riemannian Manifold
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Author : Steven Rosenberg
language : en
Publisher: Cambridge University Press
Release Date : 1997-01-09

The Laplacian On A Riemannian Manifold written by Steven Rosenberg 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 1997-01-09 with Mathematics categories.


This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.



Heat Kernels And Analysis On Manifolds Graphs And Metric Spaces


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.



Heat Kernels And Spectral Theory


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.



Stochastic Analysis On Manifolds


Stochastic Analysis On Manifolds
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Author : Elton P. Hsu
language : en
Publisher: American Mathematical Soc.
Release Date : 2002

Stochastic Analysis On Manifolds written by Elton P. Hsu 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 2002 with Mathematics categories.


Mainly from the perspective of a probabilist, Hsu shows how stochastic analysis and differential geometry can work together for their mutual benefit. He writes for researchers and advanced graduate students with a firm foundation in basic euclidean stochastic analysis, and differential geometry. He does not include the exercises usual to such texts, but does provide proofs throughout that invite readers to test their understanding. Annotation copyrighted by Book News Inc., Portland, OR.



Heat Kernels And Dirac Operators


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.



Heat Kernels For Elliptic And Sub Elliptic Operators


Heat Kernels For Elliptic And Sub Elliptic Operators
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Author : Ovidiu Calin
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-10

Heat Kernels For Elliptic And Sub Elliptic Operators written by Ovidiu Calin 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 2010-10-10 with Mathematics categories.


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.



Geometric Science Of Information


Geometric Science Of Information
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Author : Frank Nielsen
language : en
Publisher: Springer Nature
Release Date : 2021-07-14

Geometric Science Of Information written by Frank Nielsen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-14 with Computers categories.


This book constitutes the proceedings of the 5th International Conference on Geometric Science of Information, GSI 2021, held in Paris, France, in July 2021. The 98 papers presented in this volume were carefully reviewed and selected from 125 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: Probability and statistics on Riemannian Manifolds; sub-Riemannian geometry and neuromathematics; shapes spaces; geometry of quantum states; geometric and structure preserving discretizations; information geometry in physics; Lie group machine learning; geometric and symplectic methods for hydrodynamical models; harmonic analysis on Lie groups; statistical manifold and Hessian information geometry; geometric mechanics; deformed entropy, cross-entropy, and relative entropy; transformation information geometry; statistics, information and topology; geometric deep learning; topological and geometrical structures in neurosciences; computational information geometry; manifold and optimization; divergence statistics; optimal transport and learning; and geometric structures in thermodynamics and statistical physics.



Analysis And Partial Differential Equations On Manifolds Fractals And Graphs


Analysis And Partial Differential Equations On Manifolds Fractals And Graphs
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Author : Alexander Grigor'yan
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-01-18

Analysis And Partial Differential Equations On Manifolds Fractals And Graphs written by Alexander Grigor'yan and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-18 with Mathematics categories.


The book covers the latest research in the areas of mathematics that deal the properties of partial differential equations and stochastic processes on spaces in connection with the geometry of the underlying space. Written by experts in the field, this book is a valuable tool for the advanced mathematician.



Mathematical Physics Spectral Theory And Stochastic Analysis


Mathematical Physics Spectral Theory And Stochastic Analysis
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Author : Michael Demuth
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-07-08

Mathematical Physics Spectral Theory And Stochastic Analysis written by Michael Demuth 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 2014-07-08 with Mathematics categories.


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.