Invariant Spaces of Holomorphic Functions on Symmetric Siegel domains
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911606340845568 |
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| author | Calzi, Mattia |
| author_facet | Calzi, Mattia |
| contents | 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 $\mathrm{Aff}$ 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 Möbius-invariant Semi-Hilbert spaces on general domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_06058 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Invariant Spaces of Holomorphic Functions on Symmetric Siegel domains Calzi, Mattia Complex Variables Functional Analysis 46E15, 47B33, 32M15 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 $\mathrm{Aff}$ 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 Möbius-invariant Semi-Hilbert spaces on general domains. |
| title | Invariant Spaces of Holomorphic Functions on Symmetric Siegel domains |
| topic | Complex Variables Functional Analysis 46E15, 47B33, 32M15 |
| url | https://arxiv.org/abs/2211.06058 |