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Geometric Analysis On Symmetric Spaces


Geometric Analysis On Symmetric Spaces
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Geometric Analysis On Symmetric Spaces


Geometric Analysis On Symmetric Spaces
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Author : Sigurdur Helgason
language : en
Publisher: American Mathematical Society
Release Date : 2024-09-27

Geometric Analysis On Symmetric Spaces written by Sigurdur Helgason and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-27 with Mathematics categories.


This book gives the first systematic exposition of geometric analysis on Riemannian symmetric spaces and its relationship to the representation theory of Lie groups. The book starts with modern integral geometry for double fibrations and treats several examples in detail. After discussing the theory of Radon transforms and Fourier transforms on symmetric spaces, inversion formulas, and range theorems, Helgason examines applications to invariant differential equations on symmetric spaces, existence theorems, and explicit solution formulas, particularly potential theory and wave equations. The canonical multitemporal wave equation on a symmetric space is included. The book concludes with a chapter on eigenspace representations?that is, representations on solution spaces of invariant differential equations. Known for his high-quality expositions, Helgason received the 1988 Steele Prize for his earlier books Differential Geometry, Lie Groups and Symmetric Spaces and Groups and Geometric Analysis. Containing exercises (with solutions) and references to further results, this revised edition would be suitable for advanced graduate courses in modern integral geometry, analysis on Lie groups, and representation theory of Lie groups.



Geometric Analysis On Symmetric Spaces


Geometric Analysis On Symmetric Spaces
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Author : Phillip Griffiths
language : en
Publisher: American Mathematical Society(RI)
Release Date : 2008

Geometric Analysis On Symmetric Spaces written by Phillip Griffiths and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Electronic books categories.




Geometric Analysis On Symmetric Spaces


Geometric Analysis On Symmetric Spaces
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Author : Phillip Griffiths
language : en
Publisher: American Mathematical Soc.
Release Date : 1989

Geometric Analysis On Symmetric Spaces written by Phillip Griffiths 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 1989 with Education categories.


"This book gives the first systematic exposition of geometric analysis on Riemannian symmetric spaces and its relationship to the representation theory of Lie groups. The book starts with modern integral geometry for double fibrations and treats several examples in detail. After discussing the theory of Radon transforms and Fourier transforms on symmetric spaces, inversion formulas, and range theorems, Helgason examines applications to invariant differential equations on symmetric spaces, existence theorems, and explicit solution formulas, particularly potential theory and wave equations. The canonical multitemporal wave equation on a symmetric space is included. The book concludes with a chapter on eigenspace representations - that is, representations on solution spaces of invariant differential equations."--BOOK JACKET.



Harmonic Analysis And Special Functions On Symmetric Spaces


Harmonic Analysis And Special Functions On Symmetric Spaces
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Author : Gerrit Heckman
language : en
Publisher: Academic Press
Release Date : 1995-02-08

Harmonic Analysis And Special Functions On Symmetric Spaces written by Gerrit Heckman and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-02-08 with Mathematics categories.


The two parts of this sharply focused book, Hypergeometric and Special Functions and Harmonic Analysis on Semisimple Symmetric Spaces, are derived from lecture notes for the European School of Group Theory, a forum providing high-level courses on recent developments in group theory. The authors provide students and researchers with a thorough and thoughtful overview, elaborating on the topic with clear statements of definitions and theorems and augmenting these withtime-saving examples. An extensive set of notes supplements the text.Heckman and Schlichtkrull extend the ideas of harmonic analysis on semisimple symmetric spaces to embrace the theory of hypergeometric and spherical functions and show that the K-variant Eisenstein integrals for G/H are hypergeometric functions under this theory. They lead readers from the fundamentals of semisimple symmetric spaces of G/H to the frontier, including generalization, to the Riemannian case. This volume will interest harmonic analysts, those working on or applying the theory of symmetric spaces; it will also appeal to those with an interest in special functions.Extends ideas of harmonic analysis on symmetric spacesFirst treatment of the theory to include hypergeometric and spherical functionsLinks algebraic, analytic, and geometric methods



Causal Symmetric Spaces


Causal Symmetric Spaces
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Author : Joachim Hilgert
language : en
Publisher:
Release Date : 1997

Causal Symmetric Spaces written by Joachim Hilgert and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.


This book introduces researchers and graduate students to the concepts of causal symmetric spaces. To date, results of recent studies considered "standard" by specialists have not been widely published. This book brings this information to students and researchers in geometry and analysis of causal symmetric spaces. During the last several years, a fairly complete structure theory of irreducible causal symmetric spaces has emerged. This book is the first to present this theory with exhaustive proofs. The final chapters provide an introduction to the applications of this topic to harmonic analysis.



Groups And Geometric Analysis


Groups And Geometric Analysis
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Author : Sigurdur Helgason
language : en
Publisher: American Mathematical Society
Release Date : 2022-03-17

Groups And Geometric Analysis written by Sigurdur Helgason and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-17 with Mathematics categories.


Group-theoretic methods have taken an increasingly prominent role in analysis. Some of this change has been due to the writings of Sigurdur Helgason. This book is an introduction to such methods on spaces with symmetry given by the action of a Lie group. The introductory chapter is a self-contained account of the analysis on surfaces of constant curvature. Later chapters cover general cases of the Radon transform, spherical functions, invariant operators, compact symmetric spaces and other topics. This book, together with its companion volume, Geometric Analysis on Symmetric Spaces (AMS Mathematical Surveys and Monographs series, vol. 39, 1994), has become the standard text for this approach to geometric analysis. Sigurdur Helgason was awarded the Steele Prize for outstanding mathematical exposition for Groups and Geometric Analysis and Differential Geometry, Lie Groups and Symmetric Spaces.



Differential Geometry Lie Groups And Symmetric Spaces


Differential Geometry Lie Groups And Symmetric Spaces
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Author : Sigurdur Helgason
language : en
Publisher: American Mathematical Soc.
Release Date : 2001-06-12

Differential Geometry Lie Groups And Symmetric Spaces written by Sigurdur Helgason 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 2001-06-12 with Mathematics categories.


A great book ... a necessary item in any mathematical library. --S. S. Chern, University of California A brilliant book: rigorous, tightly organized, and covering a vast amount of good mathematics. --Barrett O'Neill, University of California This is obviously a very valuable and well thought-out book on an important subject. --Andre Weil, Institute for Advanced Study The study of homogeneous spaces provides excellent insights into both differential geometry and Lie groups. In geometry, for instance, general theorems and properties will also hold for homogeneous spaces, and will usually be easier to understand and to prove in this setting. For Lie groups, a significant amount of analysis either begins with or reduces to analysis on homogeneous spaces, frequently on symmetric spaces. For many years and for many mathematicians, Sigurdur Helgason's classic Differential Geometry, Lie Groups, and Symmetric Spaces has been--and continues to be--the standard source for this material. Helgason begins with a concise, self-contained introduction to differential geometry. Next is a careful treatment of the foundations of the theory of Lie groups, presented in a manner that since 1962 has served as a model to a number of subsequent authors. This sets the stage for the introduction and study of symmetric spaces, which form the central part of the book. The text concludes with the classification of symmetric spaces by means of the Killing-Cartan classification of simple Lie algebras over $\mathbb{C}$ and Cartan's classification of simple Lie algebras over $\mathbb{R}$, following a method of Victor Kac. The excellent exposition is supplemented by extensive collections of useful exercises at the end of each chapter. All of the problems have either solutions or substantial hints, found at the back of the book. For this edition, the author has made corrections and added helpful notes and useful references. Sigurdur Helgason was awarded the Steele Prize for Differential Geometry, Lie Groups, and Symmetric Spaces and Groups and Geometric Analysis.



Spaces Of Constant Curvature


Spaces Of Constant Curvature
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Author : Joseph Albert Wolf
language : en
Publisher:
Release Date : 1967

Spaces Of Constant Curvature written by Joseph Albert Wolf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Geometry, Riemannian categories.




Riemannian Geometry And Geometric Analysis


Riemannian Geometry And Geometric Analysis
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Author : Jürgen Jost
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-24

Riemannian Geometry And Geometric Analysis written by Jürgen Jost 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 2008-06-24 with Mathematics categories.


This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research. This new edition introduces and explains the ideas of the parabolic methods that have recently found such spectacular success in the work of Perelman at the examples of closed geodesics and harmonic forms. It also discusses further examples of geometric variational problems from quantum field theory, another source of profound new ideas and methods in geometry.