Montel's theorem and composition operators for analytic almost periodic functions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909946506903552 |
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| author | Andersson, Viktor |
| author_facet | Andersson, Viktor |
| contents | We consider the Banach space $H^\infty_{\mathrm{ap}}(\mathbb{C}_0)$ of bounded analytic functions on the open right half-plane $\mathbb{C}_0$ that are almost periodic on some smaller half-plane, as well as the subspace $A_{\mathrm{ap}}(\mathbb{C}_0)$ of those functions in $H^\infty_{\mathrm{ap}}(\mathbb{C}_0)$ that are uniformly continuous on $\mathbb{C}_0$. We prove a strong version of Montel's theorem for $H^\infty_{\mathrm{ap}}(\mathbb{C}_0)$ and characterize the bounded composition operators on $H^\infty_{\mathrm{ap}}(\mathbb{C}_0)$ and $A_{\mathrm{ap}}(\mathbb{C}_0)$, as well as the compact composition operators on $H^\infty_{\mathrm{ap}}(\mathbb{C}_0)$ and certain subspaces of it. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05800 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Montel's theorem and composition operators for analytic almost periodic functions Andersson, Viktor Functional Analysis Classical Analysis and ODEs Complex Variables We consider the Banach space $H^\infty_{\mathrm{ap}}(\mathbb{C}_0)$ of bounded analytic functions on the open right half-plane $\mathbb{C}_0$ that are almost periodic on some smaller half-plane, as well as the subspace $A_{\mathrm{ap}}(\mathbb{C}_0)$ of those functions in $H^\infty_{\mathrm{ap}}(\mathbb{C}_0)$ that are uniformly continuous on $\mathbb{C}_0$. We prove a strong version of Montel's theorem for $H^\infty_{\mathrm{ap}}(\mathbb{C}_0)$ and characterize the bounded composition operators on $H^\infty_{\mathrm{ap}}(\mathbb{C}_0)$ and $A_{\mathrm{ap}}(\mathbb{C}_0)$, as well as the compact composition operators on $H^\infty_{\mathrm{ap}}(\mathbb{C}_0)$ and certain subspaces of it. |
| title | Montel's theorem and composition operators for analytic almost periodic functions |
| topic | Functional Analysis Classical Analysis and ODEs Complex Variables |
| url | https://arxiv.org/abs/2512.05800 |