Analysis on Symmetric Cones

by Jacques Faraut, Adam Koranyi, Adam Kor?nyi

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, 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)

About the Author

Universite Pierre et Marie Curie, Paris

City University of New York

Table of Contents

1. Convex Cones
2. Jordan Algebras
3. Symmetric Cones and Euclidean Jordan Algebras
4. The Peirce Decomposition In a Jordan Algebra
5. Classification of Euclidean Jordan Algebras
6. Polar Decomposition and Gauss Decomposition
7. The Gamma Function of a Symmetric Cone
8. Complex Jordan Algebras
9. Tube Domains Over Convex cones
10. Symmetric Domains
11. Conical and Spherical Polynomials
12. Taylor and Laurent Series
13. Functions Spaces on Symmetric Domains
14. Invariant Differential Operators and Spherical Functions
15. Special Functions
16. Representations of Jordan Algebras and Euclidean Fourier Analysis
Bibliography

Editorial Reviews

"The detailed exposition, careful choice of organization and notation, and very helpful collection of exercises, mostly of medium difficulty, all attest to the effort put into this joint venture." —Bulletin of the London Mathematical Society

"Whenever I have a problem or I want to find a reference, I go back to this book; thus, this is the most frequent used reference in my papers, particularly in recent ones. The chapter exercises and notes are also very helpful since they outline existing results and open problems. Hence, I view this book as a very good, important, and comprehensive research monograph in mathematical literature, and I enthusiastically recommend it to all interested readers."—Mathematical Reviews

From the Publisher