Offbeat Integral Geometry On Symmetric Spaces
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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 The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for various classes of functions, far-reaching generalizations of the two-radii problem, the modern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.
Invariant Function Spaces On Homogeneous Manifolds Of Lie Groups And Applications
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Author : Mark Lʹvovich Agranovskiĭ
language : en
Publisher: American Mathematical Soc.
Release Date : 1993-01-01
Invariant Function Spaces On Homogeneous Manifolds Of Lie Groups And Applications written by Mark Lʹvovich Agranovskiĭ 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 1993-01-01 with Mathematics categories.
This book studies translation-invariant function spaces and algebras on homogeneous manifolds. The central topic is the relationship between the homogeneous structure of a manifold and the class of translation-invariant function spaces and algebras on the manifold. The author obtains classifications of translation-invariant spaces and algebras of functions on semisimple and nilpotent Lie groups, Riemann symmetric spaces, and bounded symmetric domains. When such classifications are possible, they lead in many cases to new characterizations of the classical function spaces, from the point of view of their group of admissible changes of variable. The algebra of holomorphic functions plays an essential role in these classifications when a homogeneous complex or $CR$-structure exists on the manifold. This leads to new characterizations of holomorphic functions and their boundary values for one- and multidimensional complex domains.
Complex Analysis And Dynamical Systems Ii
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Author : Lawrence Allen Zalcman
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Complex Analysis And Dynamical Systems Ii written by Lawrence Allen Zalcman 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 2005 with Mathematics categories.
This volume is a collection of papers reflecting the conference held in Nahariya, Israel in honor of Professor Lawrence Zalcman's sixtieth birthday. The papers, many written by leading authorities, range widely over classical complex analysis of one and several variables, differential equations, and integral geometry. Topics covered include, but are not limited to, these areas within the theory of functions of one complex variable: complex dynamics, elliptic functions, Kleinian groups, quasiconformal mappings, Tauberian theorems, univalent functions, and value distribution theory. Altogether, the papers in this volume provide a comprehensive overview of activity in complex analysis at the beginning of the twenty-first century and testify to the continuing vitality of the interplay between classical and modern analysis. It is suitable for graduate students and researchers interested in computer analysis and differential geometry. Information for our distributors: This book is co-published with Bar-Ilan University.
Representation Theory Complex Analysis And Integral Geometry
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Author : Bernhard Krötz
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-14
Representation Theory Complex Analysis And Integral Geometry written by Bernhard Krötz 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 2011-12-14 with Mathematics categories.
This volume targets graduate students and researchers in the fields of representation theory, automorphic forms, Hecke algebras, harmonic analysis, number theory.
Integral Geometry Of Tensor Fields
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Author : V. A. Sharafutdinov
language : en
Publisher: VSP
Release Date : 1994
Integral Geometry Of Tensor Fields written by V. A. Sharafutdinov and has been published by VSP this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
Fourier Analysis
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Author : William O. Bray
language : en
Publisher: CRC Press
Release Date : 2020-12-17
Fourier Analysis written by William O. Bray and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-17 with Mathematics categories.
Providing complete expository and research papers on the geometric and analytic aspects of Fourier analysis, this work discusses new approaches to classical problems in the theory of trigonometric series, singular integrals/pseudo-differential operators, Fourier analysis on various groups, numerical aspects of Fourier analysis and their applications, wavelets and more.
The Selected Works Of Sigurdur Helgason
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Author : Sigurdur Helgason
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
The Selected Works Of Sigurdur Helgason 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 2009 with Mathematics categories.
Collects the articles that cover invariant differential operators, geometric properties of solutions to differential equations on symmetric spaces, double fibrations in integral geometry, spherical functions and spherical transforms, duality for symmetric spaces, representation theory, and the Fourier transform on G/K.
Automorphic Forms And Related Geometry Assessing The Legacy Of I I Piatetski Shapiro
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Author : James W. Cogdell
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-04-01
Automorphic Forms And Related Geometry Assessing The Legacy Of I I Piatetski Shapiro written by James W. Cogdell 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 2014-04-01 with Mathematics categories.
This volume contains the proceedings of the conference Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro, held from April 23-27, 2012, at Yale University, New Haven, CT. Ilya I. Piatetski-Shapiro, who passed away on 21 February 2009, was a leading figure in the theory of automorphic forms. The conference attempted both to summarize and consolidate the progress that was made during Piatetski-Shapiro's lifetime by him and a substantial group of his co-workers, and to promote future work by identifying fruitful directions of further investigation. It was organized around several themes that reflected Piatetski-Shapiro's main foci of work and that have promise for future development: functoriality and converse theorems; local and global -functions and their periods; -adic -functions and arithmetic geometry; complex geometry; and analytic number theory. In each area, there were talks to review the current state of affairs with special attention to Piatetski-Shapiro's contributions, and other talks to report on current work and to outline promising avenues for continued progress. The contents of this volume reflect most of the talks that were presented at the conference as well as a few additional contributions. They all represent various aspects of the legacy of Piatetski-Shapiro.
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.
Integral Geometry And Radon Transforms
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Author : Sigurdur Helgason
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-17
Integral Geometry And Radon Transforms written by Sigurdur Helgason 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 2010-11-17 with Mathematics categories.
In this text, integral geometry deals with Radon’s problem of representing a function on a manifold in terms of its integrals over certain submanifolds—hence the term the Radon transform. Examples and far-reaching generalizations lead to fundamental problems such as: (i) injectivity, (ii) inversion formulas, (iii) support questions, (iv) applications (e.g., to tomography, partial di erential equations and group representations). For the case of the plane, the inversion theorem and the support theorem have had major applications in medicine through tomography and CAT scanning. While containing some recent research, the book is aimed at beginning graduate students for classroom use or self-study. A number of exercises point to further results with documentation. From the reviews: “Integral Geometry is a fascinating area, where numerous branches of mathematics meet together. the contents of the book is concentrated around the duality and double vibration, which is realized through the masterful treatment of a variety of examples. the book is written by an expert, who has made fundamental contributions to the area.” —Boris Rubin, Louisiana State University