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Berezin transform on real bounded symmetric domains. (English) Zbl 0965.22015
The author considers the Berezin transform on \(L^2(D)\), where \(D\) is a real bounded symmetric domain, and describes the spectral symbol of the Berezin transform under the irreducible decomposition of \(L^2(D)\). Some other properties connected with this transform, the Berezin kernel and weighted Bergman spaces are also studied.

MSC:
22E46 Semisimple Lie groups and their representations
43A85 Harmonic analysis on homogeneous spaces
32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
53C35 Differential geometry of symmetric spaces
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