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Berezin transform on real bounded symmetric domains

By Genkai Zhang

Abstract

Abstract. Let D be a bounded symmetric domain in a complex vector space VC with a real form V and D = D ∩ V = G/K be the real bounded symmetric domain in the real vector space V. We construct the Berezin kernel and consider the Berezin transform on the L2-space on D. The corresponding representation of G is then unitarily equivalent to the restriction to G of a scalar holomorphic discrete series of holomorphic functions on D and is also called the canonical representation. We find the spectral symbol of the Berezin transform under the irreducible decomposition of the L2-space

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.352.3669
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