Invariant Hilbert spaces of holomorphic functions
Copyright policy )Invariant Hilbert spaces of holomorphic functions
Summary: 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.
- University of Groningen Netherlands
Hilbert space of holomorphic functions, Hilbert spaces of continuous, differentiable or analytic functions, Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)), invariant under a group of holomorphic automorphisms, Algebras of holomorphic functions of several complex variables, Geometric theory, characteristics, transformations in context of PDEs
Hilbert space of holomorphic functions, Hilbert spaces of continuous, differentiable or analytic functions, Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)), invariant under a group of holomorphic automorphisms, Algebras of holomorphic functions of several complex variables, Geometric theory, characteristics, transformations in context of PDEs
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