Universal radial limits of meromorphic functions in the unit disk
We consider the space of meromorphic functions in the unit disk $\mathbb{D}$ and show that there exists a dense $G_{\delta }$-subset of functions having universal radial limits. Our results complement known statements about holomorphic functions and further imply the existence of meromorphic functio...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2022-09-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.352/ |
| Summary: | We consider the space of meromorphic functions in the unit disk $\mathbb{D}$ and show that there exists a dense $G_{\delta }$-subset of functions having universal radial limits. Our results complement known statements about holomorphic functions and further imply the existence of meromorphic functions having maximal cluster sets along certain subsets of $\mathbb{D}$. |
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| ISSN: | 1778-3569 |