Analysis on Symmetric Cones

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Analysis on Symmetric Cones is the first book to provide a systematic and clear introduction to the theory of symmetric cones, a subject of growing importance in number theory and multivariate analysis. Beginning with an elementary description of the Jordan algebra approach to the geometric and algebraic foundations of the theory, the book goes on to discuss harmonic analysis and special functions associated with symmetric cones, tying these results together with the study of holomorphic functions on bounded symmetric domains of tube type. Written by algebraic geometers, the book contains a detailed exposition of the spherical polynomials, multivariate hypergeometric functions, and invariant differential operators. The approach is based on Jordan algebras; all that is needed from the theory of these is developed in the first few chapters. The book will be read by students and theoreticians in pure mathematics, non-commutative harmonic analysis, Jordan algebras, and multivariate statistics.
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Product Details

  • ISBN-13: 9780198534778
  • Publisher: Oxford University Press, USA
  • Publication date: 12/28/1994
  • Series: Oxford Mathematical Monographs Series
  • Pages: 400
  • Product dimensions: 6.38 (w) x 9.50 (h) x 1.10 (d)

Meet the Author

Universite Pierre et Marie Curie, Paris

City University of New York

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Table of Contents

Ch. I Symmetric cones
Ch. II Jordan algebras
Ch. III Symmetric cones and Euclidean Jordan algebras
Ch. IV The Peirce decomposition in a Jordan algebra
Ch. V Classification of Euclidean Jordan algebras
Ch. VI Polar decomposition and Gauss decomposition
Ch. VII The gamma function of a symmetric cone
Ch. VIII Complex Jordan algebras
Ch. IX Tube domains over convex cones
Ch. X Symmetric domains of tube type
Ch. XI Conical and spherical polynomials
Ch. XII Taylor and Laurent series
Ch. XIII Function spaces on symmetric domains of tube type
Ch. XIV Invariant differential operators and spherical functions
Ch. XV Special functions
Ch. XVI Representations of Jordan algebras and Euclidean Fourier analysis
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