Complete frequencies for Koenigs domains
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910890470670336 |
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| author | Bracci, Filippo Gallardo-Gutiérrez, Eva A. Yakubovich, Dmitry |
| author_facet | Bracci, Filippo Gallardo-Gutiérrez, Eva A. Yakubovich, Dmitry |
| contents | We provide a complete characterization of those non-elliptic semigroups of holomorphic self-maps of the unit disc for which the linear span of eigenvectors of the generator of the corresponding semigroup of composition operators is weak-star dense in $H^\infty$. We also give some necessary and some sufficient conditions for completeness in $H^p$. This problem is equivalent to the completeness of the corresponding exponential functions in $H^\infty$ (in the weak-star sense) or in $H^p$ of the Koenigs domain of the semigroup. As a tool needed for the results, we introduce and study discontinuities of semigroups of holomorphic self-maps of the unit disc. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_17470 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Complete frequencies for Koenigs domains Bracci, Filippo Gallardo-Gutiérrez, Eva A. Yakubovich, Dmitry Complex Variables Functional Analysis We provide a complete characterization of those non-elliptic semigroups of holomorphic self-maps of the unit disc for which the linear span of eigenvectors of the generator of the corresponding semigroup of composition operators is weak-star dense in $H^\infty$. We also give some necessary and some sufficient conditions for completeness in $H^p$. This problem is equivalent to the completeness of the corresponding exponential functions in $H^\infty$ (in the weak-star sense) or in $H^p$ of the Koenigs domain of the semigroup. As a tool needed for the results, we introduce and study discontinuities of semigroups of holomorphic self-maps of the unit disc. |
| title | Complete frequencies for Koenigs domains |
| topic | Complex Variables Functional Analysis |
| url | https://arxiv.org/abs/2311.17470 |