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Berezin transform on line bundles over bounded symmetric domains. (English) Zbl 0946.43007

J. Lie Theory 10, No. 1, 111-126 (2000); erratum ibid. 11, No. 1, 255 (2001).
The author of this very interesting paper determines the symbol of the Berezin transform as a function of \(G\)-invariant differential operators on the line bundles over a bounded symmetric domain \(D\). In this process the author obtains an explicit formula for the generalized Harish Chandra \(C\)-function, using the Siegel domain realization of the bounded symmetric domain \(D\), and shows that these are eigenfunctions of invariant differential operators with respect to the weighted action of \(G\). The author then obtains the symbol of the Berezin transform on the compact dual of \(D\).

MSC:

43A85 Harmonic analysis on homogeneous spaces
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