Offbeat Integral Geometry On Symmetric Spaces

Author : Valery V. Volchkov,Vitaly V. Volchkov
Publisher : Springer Science & Business Media
Page : 596 pages
File Size : 41,8 Mb
Release : 2013-01-30
Category : Mathematics
ISBN : 9783034805728

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Offbeat Integral Geometry on Symmetric Spaces by Valery V. Volchkov,Vitaly V. Volchkov Pdf

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 The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for various classes of functions, far-reaching generalizations of the two-radii problem, the modern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.

Author : Semen Grigorʹevich Gindikin
Publisher : American Mathematical Soc.
Page : 372 pages
File Size : 47,5 Mb
Release : 2003
Category : Geometry, Differential
ISBN : 082183472X

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Lie Groups and Symmetric Spaces by Semen Grigorʹevich Gindikin Pdf

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.

Author : Sigurdur Helgason
Publisher : American Mathematical Society
Page : 504 pages
File Size : 52,5 Mb
Release : 2024-04-05
Category : Mathematics
ISBN : 9781470476878

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Differential Geometry and Symmetric Spaces by Sigurdur Helgason Pdf

Sigurdur Helgason's Differential Geometry and Symmetric Spaces was quickly recognized as a remarkable and important book. For many years, it was the standard text both for Riemannian geometry and for the analysis and geometry of symmetric spaces. Several generations of mathematicians relied on it for its clarity and careful attention to detail. Although much has happened in the field since the publication of this book, as demonstrated by Helgason's own three-volume expansion of the original work, this single volume is still an excellent overview of the subjects. For instance, even though there are now many competing texts, the chapters on differential geometry and Lie groups continue to be among the best treatments of the subjects available. There is also a well-developed treatment of Cartan's classification and structure theory of symmetric spaces. The last chapter, on functions on symmetric spaces, remains an excellent introduction to the study of spherical functions, the theory of invariant differential operators, and other topics in harmonic analysis. This text is rightly called a classic.

Author : Phillip Griffiths,Sigurdur Helgason
Publisher : American Mathematical Society(RI)
Page : 657 pages
File Size : 52,7 Mb
Release : 2008
Category : Electronic books
ISBN : 1470412667

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Geometric Analysis on Symmetric Spaces by Phillip Griffiths,Sigurdur Helgason Pdf

Author : Sigurdur Helgason
Publisher : American Mathematical Soc.
Page : 670 pages
File Size : 42,9 Mb
Release : 1993
Category : Mathematics
ISBN : 082187487X

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Geometric Analysis on Symmetric Spaces by Sigurdur Helgason Pdf

Author : Boris Rubin
Publisher : Cambridge University Press
Page : 595 pages
File Size : 47,8 Mb
Release : 2015-11-12
Category : Mathematics
ISBN : 9780521854597

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Introduction to Radon Transforms by Boris Rubin Pdf

A comprehensive introduction to basic operators of integral geometry and the relevant harmonic analysis for students and researchers.

Author : Sigurdur Helgason
Publisher : American Mathematical Soc.
Page : 506 pages
File Size : 42,8 Mb
Release : 1962
Category : Geometry, Differential
ISBN : 9780821873175

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Differential Geometry and Symmetric Spaces by Sigurdur Helgason Pdf

Author : Sigurdur Helgason
Publisher : American Mathematical Society(RI)
Page : 693 pages
File Size : 50,5 Mb
Release : 2014-06-06
Category : MATHEMATICS
ISBN : 1470413108

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Groups and Geometric Analysis by Sigurdur Helgason Pdf

This volume, the second of Helgason's three books on Lie groups and the geometry and analysis of symmetric spaces, is an introduction to group-theoretic methods in analysis on spaces with a group action. The first chapter deals with the three two-dimensional spaces of constant curvature, requiring only elementary methods and no Lie theory. It would be suitable for a first-year graduate course. The remainder of the book covers more advanced topics, including the work of Harish-Chandra and others, but especially that of Helgason himself. Indeed, the exposition can be seen as an account of the author's tremendous contributions to the subject. Chapter I deals with modern integral geometry and radon transforms. The second chapter examines the interconnection between Lie groups and differential operators. Chapter IV develops the theory of spherical functions on semisimple Lie groups with a certain degree of completeness, including a study of Harish-Chandra's $c$-function.

Author : Izrailʹ Moiseevich Gelʹfand,Semen Grigorʹevich Gindikin,Mark Iosifovich Graev
Publisher : American Mathematical Soc.
Page : 136 pages
File Size : 44,9 Mb
Release : 2003
Category : Integral geometry
ISBN : 0821829327

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Selected Topics in Integral Geometry by Izrailʹ Moiseevich Gelʹfand,Semen Grigorʹevich Gindikin,Mark Iosifovich Graev Pdf

The miracle of integral geometry is that it is often possible to recover a function on a manifold just from the knowledge of its integrals over certain submanifolds. The founding example is the Radon transform, introduced at the beginning of the 20th century. Since then, many other transforms were found, and the general theory was developed. Moreover, many important practical applications were discovered. The best known, but by no means the only one, being to medical tomography. This book is a general introduction to integral geometry, the first from this point of view for almost four decades. The authors, all leading experts in the field, represent one of the most influential schools in integral geometry. The book presents in detail basic examples of integral geometry problems, such as the Radon transform on the plane and in space, the John transform, the Minkowski-Funk transform, integral geometry on the hyperbolic plane and in the hyperbolic space, the horospherical transform and its relation to representations of $SL(2,\mathbb C)$, integral geometry on quadrics, etc. The study of these examples allows the authors to explain important general topics of integral geometry, such as the Cavalieri conditions, local and nonlocal inversion formulas, and overdetermined problems in integral geometry. Many of the results in the book were obtained by the authors in the course of their career-long work in integral geometry. This book is suitable for graduate students and researchers working in integral geometry and its applications.

Author : Armand Borel,Lizhen Ji
Publisher : Springer Science & Business Media
Page : 477 pages
File Size : 53,8 Mb
Release : 2006-07-25
Category : Mathematics
ISBN : 9780817644666

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Compactifications of Symmetric and Locally Symmetric Spaces by Armand Borel,Lizhen Ji Pdf

Introduces uniform constructions of most of the known compactifications of symmetric and locally symmetric spaces, with emphasis on their geometric and topological structures Relatively self-contained reference aimed at graduate students and research mathematicians interested in the applications of Lie theory and representation theory to analysis, number theory, algebraic geometry and algebraic topology

Author : Convex Geometry Special Session on Radon Transforms
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 47,5 Mb
Release : 2008
Category : Harmonic analysis
ISBN : 9780821843277

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Radon Transforms, Geometry, and Wavelets by Convex Geometry Special Session on Radon Transforms Pdf

This volume is based on two special sessions held at the AMS Annual Meeting in New Orleans in January 2007, and a satellite workshop held in Baton Rouge on January 4-5, 2007. It consists of invited expositions that together represent a broad spectrum of fields, stressing surprising interactions and connections between areas that are normally thought of as disparate. The main topics are geometry and integral transforms. On the one side are harmonic analysis, symmetric spaces,representation theory (the groups include continuous and discrete, finite and infinite, compact and non-compact), operator theory, PDE, and mathematical probability. Moving in the applied direction we encounter wavelets, fractals, and engineering topics such as frames and signal and image processing.The subjects covered in this book form a unified whole, and they stand at the crossroads of pure and applied mathematics. The articles cover a broad range in harmonic analysis, with the main themes related to integral geometry, the Radon transform, wavelets and frame theory. These themes can loosely be grouped together as follows:Frame Theory and ApplicationsHarmonic Analysis and Function SpacesHarmonic Analysis and Number TheoryIntegral Geometry and Radon TransformsMultiresolution Analysis, Wavelets, and Applications

Author : Audrey Terras
Publisher : Springer Science & Business Media
Page : 395 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461238201

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Harmonic Analysis on Symmetric Spaces and Applications II by Audrey Terras Pdf

Well, finally, here it is-the long-promised "Revenge of the Higher Rank Symmetric Spaces and Their Fundamental Domains." When I began work on it in 1977, I would probably have stopped immediately if someone had told me that ten years would pass before I would declare it "finished." Yes, I am declaring it finished-though certainly not perfected. There is a large amount of work going on at the moment as the piles of preprints reach the ceiling. Nevertheless, it is summer and the ocean calls. So I am not going to spend another ten years revising and polishing. But, gentle reader, do send me your corrections and even your preprints. Thanks to your work, there is an Appendix at the end of this volume with corrections to Volume I. I said it all in the Preface to Volume I. So I will try not to repeat myself here. Yes, the "recent trends" mentioned in that Preface are still just as recent.

Author : Lawrence Allen Zalcman,Mark Lʹvovich Agranovskiĭ,Lavi Karp,David Shoiykhet
Publisher : American Mathematical Soc.
Page : 456 pages
File Size : 43,7 Mb
Release : 2005
Category : Differentiable dynamical systems
ISBN : 9780821837092

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Complex Analysis and Dynamical Systems II by Lawrence Allen Zalcman,Mark Lʹvovich Agranovskiĭ,Lavi Karp,David Shoiykhet Pdf

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.

Author : G. Daniel Mostow
Publisher : Princeton University Press
Page : 204 pages
File Size : 47,5 Mb
Release : 1973-12-21
Category : Mathematics
ISBN : 9780691081366

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Strong Rigidity of Locally Symmetric Spaces by G. Daniel Mostow Pdf

Locally symmetric spaces are generalizations of spaces of constant curvature. In this book the author presents the proof of a remarkable phenomenon, which he calls "strong rigidity": this is a stronger form of the deformation rigidity that has been investigated by Selberg, Calabi-Vesentini, Weil, Borel, and Raghunathan. The proof combines the theory of semi-simple Lie groups, discrete subgroups, the geometry of E. Cartan's symmetric Riemannian spaces, elements of ergodic theory, and the fundamental theorem of projective geometry as applied to Tit's geometries. In his proof the author introduces two new notions having independent interest: one is "pseudo-isometries"; the other is a notion of a quasi-conformal mapping over the division algebra K (K equals real, complex, quaternion, or Cayley numbers). The author attempts to make the account accessible to readers with diverse backgrounds, and the book contains capsule descriptions of the various theories that enter the proof.

Author : Leon Ehrenpreis
Publisher : American Mathematical Soc.
Page : 508 pages
File Size : 41,6 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821811481

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Analysis, Geometry, Number Theory by Leon Ehrenpreis Pdf

This book presents the proceedings from a conference at Temple University celebrating the work of Leon Ehrenpreis, distinguished by its insistence upon getting to the heart of the mathematics and by its astonishing consistency in doing so successfully. Professor Ehrenpreis has worked in many areas of mathematics and has found connections among all of them. For example, we can find his analysis ideas in the context of number theory, geometric thinking within analysis, transcendental number theory tied to partial differential equations.The conference brought together the communities of mathematicians working in the areas of interest to Professor Ehrenpreis and allowed them to share the research inspired by his work. The collection of articles presents current research on PDE's, several complex variables, analytic number theory, integral geometry and tomography. The thinking of Professor Ehrenpreis has contributed fundamental concepts and techniques in these areas and has motivated a wealth of research results. This volume offers a survey of the fundamental principles that unified the conference and influenced the mathematics of Leon Ehrenpreis.