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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2407.10664 |
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| _version_ | 1866916324560601088 |
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| author | Cruz-Zamorano, Francisco J. |
| author_facet | Cruz-Zamorano, Francisco J. |
| contents | A complete characterization of parabolic self-maps of finite shift is given in terms of their Herglotz's representation. This improves a previous result due to Contreras, Díaz-Madrigal, and Pommerenke. We also derive some consequences for the rate of convergence of these functions to their Denjoy-Wolff point, improving a related result of Kourou, Theodosiadis, and Zarvalis for the continuous setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10664 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterization of finite shift via Herglotz's representation Cruz-Zamorano, Francisco J. Complex Variables Primary 30D05, 37F99, Secondary 30E20 A complete characterization of parabolic self-maps of finite shift is given in terms of their Herglotz's representation. This improves a previous result due to Contreras, Díaz-Madrigal, and Pommerenke. We also derive some consequences for the rate of convergence of these functions to their Denjoy-Wolff point, improving a related result of Kourou, Theodosiadis, and Zarvalis for the continuous setting. |
| title | Characterization of finite shift via Herglotz's representation |
| topic | Complex Variables Primary 30D05, 37F99, Secondary 30E20 |
| url | https://arxiv.org/abs/2407.10664 |