✦ LIBER ✦

Reproducing Kernels and Composition Series for Spaces of Vector-Valued Holomorphic Functions on Tube Domains

✍ Scribed by B. Orsted; G. Zhang

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 667 KB
Volume: 124
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1994.1104

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✦ Synopsis

We study Hilbert spaces of vector-valued holomorphic sections on tube domains 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 expansions of matrix-valued reproducing kernels. C. 1994 Academic Press. Inc.