Analysis on Symmetric Cones
Published on 29. December 1994
Book
Hardback
394 pages
978-0-19-853477-8 (ISBN)
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.
Reviews / Votes
... 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 SocietyMore details
Series
Language
English
Place of publication
Oxford
United Kingdom
Publishing group
Oxford University Press
Target group
Professional and scholarly
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 28 mm
Weight
792 gr
ISBN-13
978-0-19-853477-8 (9780198534778)
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Schweitzer Classification
Persons
Content
I. Convex cones ; II. Jordan algebras ; III. Symmetric cones and Euclidean Jordan algebras ; IV. The Peirce decomposition in a Jordan algebra ; V. Classification of Euclidean Jordan algebras ; VI. Polar decomposition and Gauss decomposition ; VII. The gamma function of a symmetric cone ; VIII. Complex Jordan algebras ; IX. Tube domains over convex cones ; X. Symmetric domains ; XI. Conical and spherical polynomials ; XII. Taylor and Laurent series ; XIII. Functions spaces on symmetric domains ; XIV. Invariant differential operators and spherical functions ; XV. Special functions ; XVI. Representations of Jordan algebras and Euclidean Fourier analysis ; Bibliography