Journal of Operator Theory

Volume 94, Issue 2, Autumn 2025 pp. 559-611.

Invariant spaces of holomorphic functions on symmetric Siegel domains

Authors: Mattia Calzi
Author institution: Dipartimento di Matematica, Universita degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy

Summary: 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 classification of the affinely-invariant semi-Hilbert spaces (satisfying some natural additional assumptions) on tube domains, and slightly improve the classification of M\"obius-invariant semi-Hilbert spaces on general domains.

DOI: http://dx.doi.org/10.7900/jot.2024feb23.2454
Keywords: Dirichlet space, symmetric domains, Wallach set, invariant spaces

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