Synopses & Reviews
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.
Review
"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
Synopsis
In no era in the history of Western art have so many artists invested so much thought and passion in the depiction of the physical conditions of the world as the nineteenth century. This volume is filled with spectacular landscape paintings by the Hudson River school artists Bierstadt (Lake
Lucerne), Church (Morning in the Tropics), Cole, and Durand. Numerous marine paintings, Heade's view of nature, several portraits by Eakins, and Homer's critically acclaimed Breezing Up (A Fair Wind) are included as well, thoughtfully presented and richly illustrated.
Description
Includes bibliographical references (p. 364-377) and index.
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