Journal of Lie Theory, Vol. 9, No. 2, pp. 383-402 (1999)

Invariant Hilbert spaces of holomorphic functions

J. Faraut and E.G.F. Thomas

Institut de Mathematiques de Jussieu (UMR 7586 du CNRS), Universite Pierre et Martie Curie, Case 247, 4 place Jussie 75252 Paris Cedex 05, France,, University of Groningen, Department of Mathematics, Postbus 800, NL-9700 AV Groningen, Netherlands,

Abstract: A Hilbert space of holomorphic functions on a complex manifold $Z$,which is invariant under a group $G$ of holomorphic automorphisms of $Z$, can be decomposed into irreducible subspaces by using Choquet theory. We give a geometric condition on $Z$ and $G$ which implies that this decomposition is multiplicity free, with application to several examples.

Keywords: complex manifold, holomorphic functions, holomorphic automorphisms, Hilbert space, irreducible subspaces, Choquet theory

Classification (MSC91): 46E20; 32M05

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