A Burns-Krantz type theorem for Blaschke products
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913861547851776 |
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| author | Moucha, Annika |
| author_facet | Moucha, Annika |
| contents | Let $f$ be a holomorphic function mapping the open unit disk into itself. We establish a boundary version of Schwarz' lemma in the spirit of a result by Burns and Krantz and provide sufficient conditions on the local behaviour of $f$ near some boundary point that forces $f$ to be a Blaschke product with predescribed critical points. For the proof, a local Julia type inequality based on Nehari's sharpening of Schwarz' lemma is established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21346 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Burns-Krantz type theorem for Blaschke products Moucha, Annika Complex Variables 30C80, 30J10 Let $f$ be a holomorphic function mapping the open unit disk into itself. We establish a boundary version of Schwarz' lemma in the spirit of a result by Burns and Krantz and provide sufficient conditions on the local behaviour of $f$ near some boundary point that forces $f$ to be a Blaschke product with predescribed critical points. For the proof, a local Julia type inequality based on Nehari's sharpening of Schwarz' lemma is established. |
| title | A Burns-Krantz type theorem for Blaschke products |
| topic | Complex Variables 30C80, 30J10 |
| url | https://arxiv.org/abs/2505.21346 |