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arXiv · 2211.06058

Invariant Spaces of Holomorphic Functions on Symmetric Siegel domains

Mattia Calzi
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Abstract

In this paper we consider a symmetric Siegel domain $D$ and some natural representations of the M\"obius group $G$ of its biholomorphisms and of the group $\mathrm{Aff}$ 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 M\"obius-invariant Semi-Hilbert spaces on general domains.

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Mattia Calzi. 2022-11-11. Invariant Spaces of Holomorphic Functions on Symmetric Siegel domains. https://doi.org/10.7900/jot.2024feb23.2454

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