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Berezin transform on real bounded symmetric domains |
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| Authors: | Genkai Zhang |
| Affiliation: | Department of Mathematics, Chalmers University of Technology and Göteborg University, S-412 96 Göteborg, Sweden |
| Abstract: | Let |
| Keywords: | Real bounded symmetric domains Jordan triples Siegel domains Berezin transform invariant differential operators unitary representations of Lie groups irreducible decomposition |
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be a bounded symmetric domain in a complex vector space 
with a real form 
and 
be the real bounded symmetric domain in the real vector space 
. We construct the Berezin kernel and consider the Berezin transform on the 
-space on 
. The corresponding representation of 
is then unitarily equivalent to the restriction to 
of a scalar holomorphic discrete series of holomorphic functions on 
and is also called the canonical representation. We find the spectral symbol of the Berezin transform under the irreducible decomposition of the 
-space.