Automorphic Carathéodory-Julia Theorem
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914633855533056 |
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| author | Kheifets, Alexander |
| author_facet | Kheifets, Alexander |
| contents | Let $w(ζ)$ be a function analytic on $\mathbb D$, $|w(ζ)|\le 1$. Let $|t_0|=1$. Assume that $w$ and $w'$ have nontangential boundary values $w_0$ and $w'_0$, respectively, at $t_0$, $|w_0|=1$. Then (Carathéodory - Julia) $t_0\dfrac{w'_0}{w_0}\ge 0$. The goal of this paper is to obtain a lower bound on this ratio if $w$ is character-automorphic with respect to a Fuchsian group (Theorem 6.1) |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03606 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Automorphic Carathéodory-Julia Theorem Kheifets, Alexander Complex Variables 30J99 (primary) 30H10, 46E22 (Secondary) Let $w(ζ)$ be a function analytic on $\mathbb D$, $|w(ζ)|\le 1$. Let $|t_0|=1$. Assume that $w$ and $w'$ have nontangential boundary values $w_0$ and $w'_0$, respectively, at $t_0$, $|w_0|=1$. Then (Carathéodory - Julia) $t_0\dfrac{w'_0}{w_0}\ge 0$. The goal of this paper is to obtain a lower bound on this ratio if $w$ is character-automorphic with respect to a Fuchsian group (Theorem 6.1) |
| title | Automorphic Carathéodory-Julia Theorem |
| topic | Complex Variables 30J99 (primary) 30H10, 46E22 (Secondary) |
| url | https://arxiv.org/abs/2401.03606 |