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OverviewThis volume, the second of Helgason's impressive 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 is remarkably accessible and 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. The treatment of analysis on compact symmetric spaces (Chapter V) includes some finite-dimensional representation theory for compact Lie groups and Fourier analysis on compact groups. Each chapter ends with exercises (with solutions given at the end of the book!) and historical notes. This book, which is new to the AMS publishing program, is an excellent example of the author's well-known clear and careful writing style. It has become the standard text for the study of spherical functions and invariant differential operators on symmetric spaces. Sigurdur Helgason was awarded the Steele Prize for Groups and Geometric Analysis and the companion volume, Differential Geometry, Lie Groups and Symmetric Spaces. Full Product DetailsAuthor: Sigurdur HelgasonPublisher: American Mathematical Society Imprint: American Mathematical Society Edition: New edition Volume: No. 83 Dimensions: Width: 18.40cm , Height: 4.10cm , Length: 26.00cm Weight: 1.394kg ISBN: 9780821826737ISBN 10: 0821826735 Pages: 667 Publication Date: 30 October 2000 Audience: College/higher education , Professional and scholarly , Undergraduate , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In stock  We have confirmation that this item is in stock with the supplier. It will be ordered in for you and dispatched immediately. Table of ContentsGeometric Fourier analysis on spaces of constant curvature Integral geometry and Radon transforms Invariant differential operators Invariants and harmonic polynomials Spherical functions and spherical transforms Analysis on compact symmetric spaces Appendix Some details Bibliography Symbols frequently used Index Errata.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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