Analysis on Symmetric Cones

Hardcover | March 1, 1995

byJacques Faraut, Adam Koranyi

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The present book is the first to treat analysis on symmetric cones in a systematic way. It starts by describing, with the simplest available proofs, the Jordan algebra approach to the geometric and algebraic foundations of the theory due to M. Koecher and his school. In subsequent parts itdiscusses harmonic analysis and special functions associated to symmetric cones; it also tries these results together with the study of holomorphic functions on bounded symmetric domains of tube type. It contains a number of new results and new proofs of old results.

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The present book is the first to treat analysis on symmetric cones in a systematic way. It starts by describing, with the simplest available proofs, the Jordan algebra approach to the geometric and algebraic foundations of the theory due to M. Koecher and his school. In subsequent parts itdiscusses harmonic analysis and special funct...

Jacques Faraut is at Universite Pierre et Marie Curie, Paris. Adam Koranyi is at City University of New York.

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Format:HardcoverDimensions:394 pages, 9.21 × 6.14 × 1.06 inPublished:March 1, 1995Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198534779

ISBN - 13:9780198534778

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Table of Contents

I. Convex conesII. Jordan algebrasIII. Symmetric cones and Euclidean Jordan algebrasIV. The Peirce decomposition in a Jordan algebraV. Classification of Euclidean Jordan algebrasVI. Polar decomposition and Gauss decompositionVII. The gamma function of a symmetric coneVIII. Complex Jordan algebrasIX. Tube domains over convex conesX. Symmetric domainsXI. Conical and spherical polynomialsXII. Taylor and Laurent seriesXIII. Functions spaces on symmetric domainsXIV. Invariant differential operators and spherical functionsXV. Special functionsXVI. Representations of Jordan algebras and Euclidean Fourier analysisBibliography

Editorial Reviews

... the present book is more carefully directed at the graduate student level, includes numerous exercises, and has its emphasis more on the harmonic analysis side. Such a presentation is much needed. The detailed exposition, careful choice of organization and notation, and very helpfulcollection of exercises, mostly of medium difficulty, all attest to the effort put into this joint venture. As a highly readable and accessible presentation of Jordan algebras and their applications to Riemannian geometry and harmonic analysis, the book is strongly recommended to all analysts(starting at graduate level) working in the multi-variable setting of symmetric spaces and Lie groups. Bulletin of the London Mathematical Society