[Groups and Geometric Analysis (Integral Geometry, Invariant Differential Operators and Spherical Functions).] EBOOK / PDF

Groups and Fourier analysis Compact Groups Each Chapter Ends groups Each chapter ends 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.

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Groups and Geometric Analysis (Integral Geometry, Invariant Differential Operators and Spherical Functions).This volume the second of helgason's impressive three books on ie groups and impressive three books on Lie groups and 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 reuiring only elementary methods and no Lie theory It is remarkably accessible and be suitable for a first year graduate course The remainder of the book covers advanced topics including the the covers advanced topics including the of Harish Chandra and others but especially that of Helgason himself.

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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 including a study of Harish c function The treatment of analysis on compact symmetric spaces Chapter V includes some finite dimensional representation theory for compact Lie.