Analysis On Non Riemannian Symmetric Spaces
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Analysis On Non Riemannian Symmetric Spaces
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Author : Mogens Flensted-Jensen
language : en
Publisher: American Mathematical Soc.
Release Date : 1986
Analysis On Non Riemannian Symmetric Spaces written by Mogens Flensted-Jensen 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 1986 with Mathematics categories.
Harmonic analysis on Riemannian semi simple symmetric spaces and on special types of non-Riemannian semi simple symmetric spaces are well-established theories. This book presents a systematic treatment of the basic problems on semi simple symmetric spaces and a discussion of some of the more important recent developments in the field.
Analysis On Non Riemannian Symmetric Spaces
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Author : Mogens Flensted-Jensen
language : en
Publisher: American Mathematical Soc.
Release Date : 1986-12-31
Analysis On Non Riemannian Symmetric Spaces written by Mogens Flensted-Jensen 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 1986-12-31 with Mathematics categories.
Harmonic analysis on Riemannian semisimple symmetric spaces and on special types of non-Riemannian semisimple symmetric spaces are well-established theories. This book presents a systematic treatment of the basic problems on semisimple symmetric spaces and a discussion of some of the more important recent developments in the field. The author's primary contribution has been his idea of how to construct the discrete series for such a space. In this book a fundamental role is played by the ideas behind that construction, namely the duality principle, the orbit picture related to it, and the definition of representations by means of distributions on the orbits. Intended as a text at the upper graduate level, the book assumes a basic knowledge of Fourier analysis, differential geometry, and functional analysis. In particular, the reader should have a good knowledge of the general theory of real and complex Lie algebras and Lie groups and of the root and weight theories for semisimple Lie algebras and Lie groups.
Semisimple Groups And Riemannian Symmetric Spaces
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Author : Armand Borel
language : en
Publisher: Springer
Release Date : 1998-12-15
Semisimple Groups And Riemannian Symmetric Spaces written by Armand Borel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-15 with Mathematics categories.
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
Spaces Of Constant Curvature
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Author : Joseph A. Wolf
language : en
Publisher: American Mathematical Society
Release Date : 2023-06-05
Spaces Of Constant Curvature written by Joseph A. Wolf 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 2023-06-05 with Mathematics categories.
This book is the sixth edition of the classic Spaces of Constant Curvature, first published in 1967, with the previous (fifth) edition published in 1984. It illustrates the high degree of interplay between group theory and geometry. The reader will benefit from the very concise treatments of riemannian and pseudo-riemannian manifolds and their curvatures, of the representation theory of finite groups, and of indications of recent progress in discrete subgroups of Lie groups. Part I is a brief introduction to differentiable manifolds, covering spaces, and riemannian and pseudo-riemannian geometry. It also contains a certain amount of introductory material on symmetry groups and space forms, indicating the direction of the later chapters. Part II is an updated treatment of euclidean space form. Part III is Wolf's classic solution to the Clifford–Klein Spherical Space Form Problem. It starts with an exposition of the representation theory of finite groups. Part IV introduces riemannian symmetric spaces and extends considerations of spherical space forms to space forms of riemannian symmetric spaces. Finally, Part V examines space form problems on pseudo-riemannian symmetric spaces. At the end of Chapter 12 there is a new appendix describing some of the recent work on discrete subgroups of Lie groups with application to space forms of pseudo-riemannian symmetric spaces. Additional references have been added to this sixth edition as well.
Offbeat Integral Geometry On Symmetric Spaces
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Author : Valery V. Volchkov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-30
Offbeat Integral Geometry On Symmetric Spaces written by Valery V. Volchkov 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 2013-01-30 with Mathematics categories.
The book demonstrates the development of integral geometry on domains of homogeneous spaces since 1990. It covers a wide range of topics, including analysis on multidimensional Euclidean domains and Riemannian symmetric spaces of arbitrary ranks as well as recent work on phase space and the Heisenberg group. The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for various classes of functions, far-reaching generalizations of the two-radii problem, the modern versions of the Pompeiu problem, and explicit reconstruction formulae in problems of integral geometry. These results are intriguing and useful in various fields of contemporary mathematics. The proofs given are “minimal” in the sense that they involve only those concepts and facts which are indispensable for the essence of the subject. Each chapter provides a historical perspective on the results presented and includes many interesting open problems. Readers will find this book relevant to harmonic analysis on homogeneous spaces, invariant spaces theory, integral transforms on symmetric spaces and the Heisenberg group, integral equations, special functions, and transmutation operators theory.
Representation Theory And Noncommutative Harmonic Analysis Ii
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Author : A.A. Kirillov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Representation Theory And Noncommutative Harmonic Analysis Ii written by A.A. Kirillov 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 2013-03-09 with Mathematics categories.
At first only elementary functions were studied in mathematical analysis. Then new functions were introduced to evaluate integrals. They were named special functions: integral sine, logarithms, the exponential function, the prob ability integral and so on. Elliptic integrals proved to be the most important. They are connected with rectification of arcs of certain curves. The remarkable idea of Abel to replace these integrals by the corresponding inverse functions led to the creation of the theory of elliptic functions. They are doubly periodic functions of a complex variable. This periodicity has led to consideration of the lattice of periods and to linear-fractional trans formations of the complex plane which leave this lattice invariant. The group of these transformations is isomorphic to the quotient group of the group 8L(2, Z) of unimodular matrices of the second order with integral elements with respect to its center. Investigation of properties of elliptic functions led to the study of automorphic functions and forms. This gave the first connec tion between the theory of groups and this important class of functions. The further development of the theory of automorphic functions was related to geometric concepts connected with the fact that the group of linear-fractional transformations with real elements can be realized as the group of motions of th the Lobachevskij plane. We also note that at the beginning of the 19 century Gauss used the group 8L(2, Z) in his papers on the theory of indeterminate quadratic forms.
Lie Groups And Symmetric Spaces
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Author : Semen Grigorʹevich Gindikin
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Lie Groups And Symmetric Spaces written by Semen Grigorʹevich Gindikin 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.
The book contains survey and research articles devoted mainly to geometry and harmonic analysis of symmetric spaces and to corresponding aspects of group representation theory. The volume is dedicated to the memory of Russian mathematician, F. I. Karpelevich (1927-2000). Of particular interest are the survey articles by Sawyer on the Abel transform on noncompact Riemannian symmetric spaces, and by Anker and Ostellari on estimates for heat kernels on such spaces, as well as thearticle by Bernstein and Gindikin on integral geometry for families of curves. There are also many research papers on topics of current interest. The book is suitable for graduate students and research mathematicians interested in harmonic analysis and representation theory.
Causal Symmetric Spaces
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Author : Gestur Olafsson
language : en
Publisher: Academic Press
Release Date : 1996-09-11
Causal Symmetric Spaces written by Gestur Olafsson and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-09-11 with Mathematics categories.
This book is intended to introduce 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 seeks to bring this information to students and researchers in geometry and analysis on causal symmetric spaces.Includes the newest results in harmonic analysis including Spherical functions on ordered symmetric space and the holmorphic discrete series and Hardy spaces on compactly casual symmetric spacesDeals with the infinitesimal situation, coverings of symmetric spaces, classification of causal symmetric pairs and invariant cone fieldsPresents basic geometric properties of semi-simple symmetric spacesIncludes appendices on Lie algebras and Lie groups, Bounded symmetric domains (Cayley transforms), Antiholomorphic Involutions on Bounded Domains and Para-Hermitian Symmetric Spaces
Computer Vision And Mathematical Methods In Medical And Biomedical Image Analysis
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Author : Milan Sonka
language : en
Publisher: Springer
Release Date : 2014-03-12
Computer Vision And Mathematical Methods In Medical And Biomedical Image Analysis written by Milan Sonka and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-12 with Computers categories.
Medical imaging and medical image analysisare rapidly developing. While m- ical imaging has already become a standard of modern medical care, medical image analysis is still mostly performed visually and qualitatively. The ev- increasing volume of acquired data makes it impossible to utilize them in full. Equally important, the visual approaches to medical image analysis are known to su?er from a lack of reproducibility. A signi?cant researche?ort is devoted to developing algorithms for processing the wealth of data available and extracting the relevant information in a computerized and quantitative fashion. Medical imaging and image analysis are interdisciplinary areas combining electrical, computer, and biomedical engineering; computer science; mathem- ics; physics; statistics; biology; medicine; and other ?elds. Medical imaging and computer vision, interestingly enough, have developed and continue developing somewhat independently. Nevertheless, bringing them together promises to b- e?t both of these ?elds. We were enthusiastic when the organizers of the 2004 European Conference on Computer Vision (ECCV) allowed us to organize a satellite workshop devoted to medical image analysis.