Analysis on Symmetric Cones

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.