Geometric analysis on symmetric spaces
著者
書誌事項
Geometric analysis on symmetric spaces
（Mathematical surveys and monographs, v. 39）
American Mathematical Society, c1994
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注記
Includes bibliographical references (p. 581-601) and index
内容説明・目次
内容説明
This book 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 new book would be suitable for advanced graduate courses in modern integral geometry, analysis on Lie groups, or representation theory of semisimple Lie groups.
目次
- 1. A duality in integral geometry
- 2. A duality for symmetric spaces
- 3. The Fourier transform on a symmetric space
- 4. The Radon transform on X and on X[o. Range questions
- 5. Differential equations on symmetric spaces
- 6. Eigenspace representations
- 7. Solutions to exercises
- Bibliography
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