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Full Description
The purpose of this book is to give a thorough treatment of the harmonic analysis of spherical functions on symmetric spaces. The theory was originally created by Harish-Chandra in the late 1950's and important additional contributions were made by many others in the succeeding years. The book attempts to give a definite treatment of these results from the spectral theoretic viewpoint. The harmonic analysis of spherical functions treated here contains the essentials of large parts of harmonic analysis of more general functions on semisimple Lie groups. Since the latter involves many additional technical complications, it will be very illuminating for any potential student of general harmonic analysis to see how the basic ideas emerge in the context of spherical functions. With this in mind, an attempt has been made only to use those methods (as far as possible) which generalize. Mathematicians and graduate students as well as mathematical physicists interested in semisimple Lie groups, homogeneous spaces, representations and harmonic analysis will find this book stimulating.
Contents
Contents: The Concept of a Spherical Function; Structure of Semisimple Lie Groups and Differential Operators on Them; The Elementary Spherical Functions; The Harish-Chandra Series for and the c-Function; Asymptotic Behaviour of Elementary Spherical Functions; The L2-Theory. The Harish-Chandra Transform on the Schwartz Space of G//K; LP-Theory of Harish-Chandra Transform. Fourier Analysis on the Spaces CP(G//K); Bibliography; Subject Index.
