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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.19181 |
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| _version_ | 1866909725899096064 |
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| author | Deterding, Stephen |
| author_facet | Deterding, Stephen |
| contents | Let $U \subseteq \mathbb C$ be bounded and open. For $0 < α< 1$, $A_α(U)$ is the set of functions in the little Lipschitz class with exponent $α$ that are analytic in a neighborhood of $U$. We consider three conditions, motivated by the properties of bounded point derivations, that show how the functions in $A_α(U)$ can have additional analytic structure than would otherwise be expected. We prove an implication between conditions $(c)$ and $(b)$ and show that there is no implication between conditions $(a)$ and $(c)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_19181 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analytic structure in spaces of Lipschitz functions Deterding, Stephen Complex Variables 30E25 (Primary), 30D40, 30H99 Let $U \subseteq \mathbb C$ be bounded and open. For $0 < α< 1$, $A_α(U)$ is the set of functions in the little Lipschitz class with exponent $α$ that are analytic in a neighborhood of $U$. We consider three conditions, motivated by the properties of bounded point derivations, that show how the functions in $A_α(U)$ can have additional analytic structure than would otherwise be expected. We prove an implication between conditions $(c)$ and $(b)$ and show that there is no implication between conditions $(a)$ and $(c)$. |
| title | Analytic structure in spaces of Lipschitz functions |
| topic | Complex Variables 30E25 (Primary), 30D40, 30H99 |
| url | https://arxiv.org/abs/2501.19181 |