Table of Contents

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

Reviews

... 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