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