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.

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