Reproducing kernels and composition series for spaces of vector-valued holomorphic functions

Bent Ørsted and Genkai Zhang

Vol. 171 (1995), No. 2, 493–510

DOI: 10.2140/pjm.1995.171.493

Abstract

We calculate the norm of each K-type in a vector-valued Hilbert space of holomorphic functions on a tube domain of type I. As a consequence we get composition series of the analytic continuation of certain holomorphic discrete series and an expansion relative to K of the matrix-valued reproducing kernel.

Mathematical Subject Classification 2000

Primary: 22E46

Secondary: 32M15, 46E22

Milestones

Received: 16 July 1993

Revised: 3 November 1993

Published: 1 December 1995