MARTIN BOUNDARIES FOR REAL SEMISIMPLE LIE-GROUPS

We construct the Martin boundaries for symmetric spaces of noncompact type X=G/K, where G is a real semisimple Lie group with a finite cente r. This work is a generalization of a result of Dynkin who constructed them in the SL(n, C) case. The main result is an explicit form of the Martin kernel. It is obtained by means of investigation of asymptotic s of Green's functions and zonal spherical functions on G. Comparison of the Martin compactification and the Satake and Karpelevich compacti fications is presented. Finally we give an explicit form of our constr uction for the Cartan domain of the type 1. In conclusion we discuss a n application of our approach to the scattering problem of the quantum Calogero-Moser system and a generalization to the quantum and p-adic groups. (C) 1994 Academic Press, Inc.