Spectra of infinitesimal generators of composition semigroups on weighted Bergman spaces induced by doubling weights
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929734943768576 |
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| author | Qian, Ruishen Wu, Fanglei Wulan, Hasi |
| author_facet | Qian, Ruishen Wu, Fanglei Wulan, Hasi |
| contents | Suppose $(C_t)_{t\geq0}$ is the composition semigroup induced by a one-parameter semigroup $(φ_t)_{t\geq0}$ of analytic self-maps of the unit disk. The main purpose of the paper is to investigate the spectrum of the infinitesimal generator of $(C_t)_{t\geq0}$ acting on the weighted Bergman space induced by doubling weights, provided $(φ_t)_{t\geq0}$ is elliptic. The method applied is a certain spectral mapping theorem and a characterization of the spectra of certain composition operators. Eventual norm-continuity of $(C_t)_{t\geq0}$ also plays an important role, which can be depicted in terms of studying the difference of two distinct composition operators. As a byproduct, we also characterize a certain compact integral operator that is closely related to the resolvent of the infinitesimal generator of $(C_t)_{t\geq0}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13662 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectra of infinitesimal generators of composition semigroups on weighted Bergman spaces induced by doubling weights Qian, Ruishen Wu, Fanglei Wulan, Hasi Functional Analysis Complex Variables Suppose $(C_t)_{t\geq0}$ is the composition semigroup induced by a one-parameter semigroup $(φ_t)_{t\geq0}$ of analytic self-maps of the unit disk. The main purpose of the paper is to investigate the spectrum of the infinitesimal generator of $(C_t)_{t\geq0}$ acting on the weighted Bergman space induced by doubling weights, provided $(φ_t)_{t\geq0}$ is elliptic. The method applied is a certain spectral mapping theorem and a characterization of the spectra of certain composition operators. Eventual norm-continuity of $(C_t)_{t\geq0}$ also plays an important role, which can be depicted in terms of studying the difference of two distinct composition operators. As a byproduct, we also characterize a certain compact integral operator that is closely related to the resolvent of the infinitesimal generator of $(C_t)_{t\geq0}$. |
| title | Spectra of infinitesimal generators of composition semigroups on weighted Bergman spaces induced by doubling weights |
| topic | Functional Analysis Complex Variables |
| url | https://arxiv.org/abs/2405.13662 |