Analysis on Symmetric Cones
Series: Oxford Mathematical Monographs;
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Product details:
- Publisher Clarendon Press
- Date of Publication 29 December 1994
- ISBN 9780198534778
- Binding Hardback
- No. of pages394 pages
- Size 241x160x27 mm
- Weight 699 g
- Language English 0
Categories
Short description:
This book provides researchers with the first full treatment of the analysis of symmetric cones. Beginning with a description of the Jordan algebra approach to the geometric and algebraic foundations of the theory, the authors move on to a discussion of harmonic analysis and special functions associated with symmetric cones. These results are tied together with a study of holomorphic functions on bounded symmetric domains of tube type. The book contains many new results, as well as new proofs of old results, and includes exercises suitable for graduate work.
MoreLong description:
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 it discusses 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.
... 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 helpful collection 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
Table of Contents:
Convex cones
Jordan algebras
Symmetric cones and Euclidean Jordan algebras
The Peirce decomposition in a Jordan algebra
Classification of Euclidean Jordan algebras
Polar decomposition and Gauss decomposition
The gamma function of a symmetric cone
Complex Jordan algebras
Tube domains over convex cones
Symmetric domains
Conical and spherical polynomials
Taylor and Laurent series
Functions spaces on symmetric domains
Invariant differential operators and spherical functions
Special functions
Representations of Jordan algebras and Euclidean Fourier analysis
Bibliography
