Eigenvalues for Infinitesimal Generators of Semigroups of Composition Operators
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917489575723008 |
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| author | Kourou, Maria Theodosiadis, Eleftherios K. Zarvalis, Konstantinos |
| author_facet | Kourou, Maria Theodosiadis, Eleftherios K. Zarvalis, Konstantinos |
| contents | We study the eigenvalues for infinitesimal generators of semigroups of composition operators acting on Hardy spaces, Bergman spaces, and the Dirichlet space. Such semigroups are induced by semigroups of holomorphic functions. Depending on the type of the holomorphic semigroup and the Euclidean geometry of its Koenigs domain, we find containment relations as well as sufficient conditions for the characterization of the point spectrum of the induced infinitesimal generator. For the Dirichlet space we study all types of non-elliptic semigroups whereas for the Hardy and Bergman spaces we work on parabolic semigroups extending the work of Betsakos in the hyperbolic case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_00666 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Eigenvalues for Infinitesimal Generators of Semigroups of Composition Operators Kourou, Maria Theodosiadis, Eleftherios K. Zarvalis, Konstantinos Complex Variables Functional Analysis 47B33, 47D06, 30D05 We study the eigenvalues for infinitesimal generators of semigroups of composition operators acting on Hardy spaces, Bergman spaces, and the Dirichlet space. Such semigroups are induced by semigroups of holomorphic functions. Depending on the type of the holomorphic semigroup and the Euclidean geometry of its Koenigs domain, we find containment relations as well as sufficient conditions for the characterization of the point spectrum of the induced infinitesimal generator. For the Dirichlet space we study all types of non-elliptic semigroups whereas for the Hardy and Bergman spaces we work on parabolic semigroups extending the work of Betsakos in the hyperbolic case. |
| title | Eigenvalues for Infinitesimal Generators of Semigroups of Composition Operators |
| topic | Complex Variables Functional Analysis 47B33, 47D06, 30D05 |
| url | https://arxiv.org/abs/2508.00666 |