manuscripta mathematica

, Volume 97, Issue 3, pp 371–388

Berezin transform on¶compact Hermitian symmetric spaces

  • Genkai Zhang

DOI: 10.1007/s002290050109

Cite this article as:
Zhang, G. manuscripta math. (1998) 97: 371. doi:10.1007/s002290050109


Let X=G* be a compact Hermitian symmetric space. We study the Berezin transform on L2(X) and calculate its spectrum under the decomposition of L2(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.

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

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Genkai Zhang
    • 1
  1. 1.Department of Mathematics, University of Karlstad, S-651 88 Karlstad, Sweden. e-mail: genkai.zhang@hks.seSE