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Product Description: Concentrating on complete simply connected two-dimensional manifolds with constant curvature, Topics in Harmonic Analysis on Homogeneous Spaces is a brief and elementary presentation of the subject. Treating the results of recent work in this highly active field, the author offers numerous proofs illustrating harmonic analysis on symmetric spaces...read more

Product Description: This book deals with harmonic analysis on the complete simply connected two-dimensional manifolds of constant curvature (the Euclidean plane, the two-sphere and the non-Euclidean plane). The treatment is elementary and Lie group theory is not required...read more

Product Description: This 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...read more (view table of contents, read Amazon.com's description)

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Product Description: The first edition of this book has been out of print for some time and I have decided to follow the publisher's kind suggestion to prepare a new edition. Many examples with explicit inversion formulas and range theo­ rems have been added, and the group-theoretic viewpoint emphasized...read more

This author gives the first systematic exposition of geometric analysis on Riemannian symmetric spaces and its relationship to the representation theory of semisimple Lie groups. The book starts with modern integral geometry for double fibrations and treats several examples in detail. After discussing the theory of Radon transforms and Fourier transforms on symmetric spaces, Helgason examines applications to invariant differential equations on symmetric spaces, particularly potential theory and wave equations. The book concludes with a chapter on eigenspace representations--that is, representations on solution spaces of invariant differential equations. Known for his high-quality expositions, Helgason received the 1988 AMS Steele Prize for his earlier books Differential Geometry, Lie Groups and Symmetric Spaces and Groups and Geometric Analysis. Containing exercises (with solutions) and references to further results, this book would be suitable for advanced graduate courses in modern integral geometry, analysis on Lie groups, or representation theory of semisimple Lie groups.

Product Description: 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...read more