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Berezin Kernels of Tube Domains

✍ Scribed by G. van Dijk; M. Pevzner

Book ID
102587610
Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
170 KB
Volume
181
Category
Article
ISSN
0022-1236

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✦ Synopsis

We study the Berezin kernel decomposition into positive-definite spherical functions on real forms of tube domains. In other words, we obtain, for all tube domains associated to causal pairs (G, H), the decomposition of holomorphic discrete series representations of G when restricted to the ``fully restrictive'' subgroup H.

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Reproducing Kernels and Composition Series for Spaces of Vector-Valued Holomorphic Functions on Tube Domains
✍ B. Orsted; G. Zhang πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 667 KB

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 contin