Analysis on Symmetric Cones
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.
1101402809
Analysis on Symmetric Cones
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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Analysis on Symmetric Cones

Analysis on Symmetric Cones

Analysis on Symmetric Cones

Analysis on Symmetric Cones

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Overview

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.

Product Details

ISBN-13: 9780198534778
Publisher: Oxford University Press
Publication date: 02/02/1995
Series: Oxford Mathematical Monographs
Pages: 394
Product dimensions: 9.08(w) x 6.42(h) x 1.32(d)

About the Author

Universite Pierre et Marie Curie, Paris

City University of New York

Table of Contents

1. Convex Cones2. Jordan Algebras3. Symmetric Cones and Euclidean Jordan Algebras4. The Peirce Decomposition In a Jordan Algebra5. Classification of Euclidean Jordan Algebras6. Polar Decomposition and Gauss Decomposition7. The Gamma Function of a Symmetric Cone8. Complex Jordan Algebras9. Tube Domains Over Convex cones10. Symmetric Domains11. Conical and Spherical Polynomials12. Taylor and Laurent Series13. Functions Spaces on Symmetric Domains14. Invariant Differential Operators and Spherical Functions15. Special Functions16. Representations of Jordan Algebras and Euclidean Fourier AnalysisBibliography
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