REPRODUCING KERNELS AND COMPOSITION SERIES FOR SPACES OF VECTOR-VALUED HOLOMORPHIC-FUNCTIONS ON TUBE DOMAINS

We study Hilbert spaces of vector-valued holomorphic sections on tube dom,ins of type II and III. We consider some small representations of the maximal compact subgroups and calculate the norm of each K-type in the Hilbert spaces. As a consequence we get composition series of the analytic continuations of certain holomorphic discrete series and exp ansions of matrix-valued reproducing kernels. (C) 1994 Academic Press, Inc.