Representations, characters, and spherical functions associated to causal symmetric spaces

In this paper we study spherical unitary highest weight representations ass ociated to a compactly causal symmetric space and use the results to prove estimates for the corresponding spherical functions of the c-dual non-compa ctly causal symmetric space. Such estimates turn out to be useful in determ ining the spectra of the associated weighted Bergman spaces. (C) 1999 Acade mic Press.