Invariant Spaces of Holomorphic Functions on Symmetric Siegel domains

2022/11/11 by Calzi, Mattia
#32M15 #46E15 #47B33 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2211.06058

Abstract

In this paper we consider a symmetric Siegel domain D and some natural representations of the Möbius group G of its biholomorphisms and of the group Aff of its affine biholomorphisms. We provide a complete classification of the affinely-invariant semi-Hilbert spaces (satisfying some natural additional assumptions) on tube domains, and improve the classification of Möbius-invariant Semi-Hilbert spaces on general domains.

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