The Berezin transform and invariant differential operators. (English) Zbl 0843.32019
The authors study the Berezin calculus of operators, particularly the Berezin transform, on any bounded, symmetric domain. They are able to express the Berezin transform in terms of certain invariant differential operators.
Along the way, the authors provide a nice introduction to reproducing kernels, Berezin theory, mathematical quantization, and analysis on bounded symmetric domains.
As well as providing a new point of view on the Berezin transform, this paper will serve as a useful resource.
Along the way, the authors provide a nice introduction to reproducing kernels, Berezin theory, mathematical quantization, and analysis on bounded symmetric domains.
As well as providing a new point of view on the Berezin transform, this paper will serve as a useful resource.
Reviewer: S.G.Krantz (St.Louis)
MSC:
| 32M15 | Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) |
| 47N50 | Applications of operator theory in the physical sciences |
| 32A30 | Other generalizations of function theory of one complex variable |
| 43A85 | Harmonic analysis on homogeneous spaces |
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