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.
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