Offbeat Integral Geometry On Symmetric Spaces

Author : Valery V. Volchkov
Publisher : Springer Science & Business Media
ISBN 13 : 3034805721
Total Pages : 596 pages
Book Rating : 4.28/5 ( download)

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Download or read book Offbeat Integral Geometry on Symmetric Spaces written by Valery V. Volchkov and published by Springer Science & Business Media. This book was released on 2013-01-30 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for various classes of functions, far-reaching generalizations of the two-radii problem, the modern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.
ISBN 13 : 9780821834725
Total Pages : 372 pages
Book Rating : 4.2X/5 ( download)

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Download or read book Lie Groups and Symmetric Spaces written by Semen Grigorʹevich Gindikin and published by American Mathematical Soc.. This book was released on 2003 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Phillip Griffiths
Publisher : American Mathematical Society(RI)
ISBN 13 : 9781470412661
Total Pages : 657 pages
Book Rating : 4.67/5 ( download)

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Download or read book Geometric Analysis on Symmetric Spaces written by Phillip Griffiths and published by American Mathematical Society(RI). This book was released on 2008 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Sigurdur Helgason
Publisher : American Mathematical Society
ISBN 13 : 1470476878
Total Pages : 504 pages
Book Rating : 4.78/5 ( download)

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Download or read book Differential Geometry and Symmetric Spaces written by Sigurdur Helgason and published by American Mathematical Society. This book was released on 2024-04-05 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Sigurdur Helgason
Publisher : American Mathematical Soc.
ISBN 13 : 9780821874875
Total Pages : 670 pages
Book Rating : 4.7X/5 ( download)

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Download or read book Geometric Analysis on Symmetric Spaces written by Sigurdur Helgason and published by American Mathematical Soc.. This book was released on 1993 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Boris Rubin
Publisher : Cambridge University Press
ISBN 13 : 0521854598
Total Pages : 595 pages
Book Rating : 4.97/5 ( download)

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Download or read book Introduction to Radon Transforms written by Boris Rubin and published by Cambridge University Press. This book was released on 2015-11-12 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to basic operators of integral geometry and the relevant harmonic analysis for students and researchers.

Author : Sigurdur Helgason
Publisher : American Mathematical Society(RI)
ISBN 13 : 9781470413101
Total Pages : 693 pages
Book Rating : 4.08/5 ( download)

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Download or read book Groups and Geometric Analysis written by Sigurdur Helgason and published by American Mathematical Society(RI). This book was released on 2014-06-06 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : American Mathematical Soc.
ISBN 13 : 9780821829325
Total Pages : 136 pages
Book Rating : 4.27/5 ( download)

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Download or read book Selected Topics in Integral Geometry written by Izrailʹ Moiseevich Gelʹfand and published by American Mathematical Soc.. This book was released on 2003 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Sigurdur Helgason
Publisher : American Mathematical Soc.
ISBN 13 : 0821873172
Total Pages : 506 pages
Book Rating : 4.75/5 ( download)

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Download or read book Differential Geometry and Symmetric Spaces written by Sigurdur Helgason and published by American Mathematical Soc.. This book was released on 1962 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Audrey Terras
Publisher : Springer Science & Business Media
ISBN 13 : 146123820X
Total Pages : 395 pages
Book Rating : 4.01/5 ( download)

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Download or read book Harmonic Analysis on Symmetric Spaces and Applications II written by Audrey Terras and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.