Berezin transform on¶compact Hermitian symmetric spaces


Let X=G * be a compact Hermitian symmetric space. We study the Berezin transform on L 2(X) and calculate its spectrum under the decomposition of L 2(X) into the irreducible representations of G *. As applications we find the expansion of powers of the canonical polynomial (Bergman reproducing kernel for the canonical line bundle) in terms of the spherical polynomials on X, and we find the irreducible decomposition of tensor products of Bergman spaces on X.

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Received: 10 September 1996 / Revised version: 10 September 1997

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Zhang, G. Berezin transform on¶compact Hermitian symmetric spaces. manuscripta math. 97, 371–388 (1998).

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  • Mathematics Subject Classification (1991):22E46, 47B38