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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.02522 |
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| _version_ | 1866914900776845312 |
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| author | Deterding, Stephen |
| author_facet | Deterding, Stephen |
| contents | Let $U$ be a bounded open subset of the complex plane and let $A_α(U)$ denote the set of functions analytic on $U$ that also belong to the little Lipschitz class with Lipschitz exponent $α$. It is shown that if $A_α(U)$ admits a bounded point derivation at $x \in \partial U$, then there is an approximate Taylor Theorem for $A_α(U)$ at $x$. This extends and generalizes known results concerning bounded point derivations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02522 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximate Taylor theorem for analytic Lipschitz functions Deterding, Stephen Complex Variables Functional Analysis Let $U$ be a bounded open subset of the complex plane and let $A_α(U)$ denote the set of functions analytic on $U$ that also belong to the little Lipschitz class with Lipschitz exponent $α$. It is shown that if $A_α(U)$ admits a bounded point derivation at $x \in \partial U$, then there is an approximate Taylor Theorem for $A_α(U)$ at $x$. This extends and generalizes known results concerning bounded point derivations. |
| title | Approximate Taylor theorem for analytic Lipschitz functions |
| topic | Complex Variables Functional Analysis |
| url | https://arxiv.org/abs/2408.02522 |