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Geometric analysis and symmetric spaces / Sigurdur Helgason

Auteur principal : Helgason, Sigurdur, 1927-, AuteurType de document : MonographieCollection : Mathematical surveys and monographs, 39Langue : anglais.Pays : Etats Unis.Éditeur : Providence : American Mathematical Society, 1994Description : 1 vol. (xiv-611 p.) ; 27 cmISBN : 9780821815380.ISSN : 0885-4653.Bibliographie : Bibliogr. p. 581-601. Index.Sujet MSC : 43A85, Abstract harmonic analysis, Harmonic analysis on homogeneous spaces
22E46, Lie groups, Semisimple Lie groups and their representations
53C35, Global differential geometry, Differential geometry of symmetric spaces
53C65, Global differential geometry, Integral geometry; differential forms, currents, etc.
En-ligne : Edition 2008 (Google) | MathScinet | AMS
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Bibliogr. p. 581-601. Index

This book gives the first systematic exposition of geometric analysis on Riemannian symmetric spaces and its relationship to the representation theory of 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, inversion formulas, and range theorems, Helgason examines applications to invariant differential equations on symmetric spaces, existence theorems, and explicit solution formulas, particularly potential theory and wave equations. The canonical multitemporal wave equation on a symmetric space is included. 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 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 revised edition would be suitable for advanced graduate courses in modern integral geometry, analysis on Lie groups, and representation theory of Lie groups. (source : AMS)

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