A note on the removability of totally disconnected sets for analytic functions
UDC 517.537.38 We prove that each totally disconnected closed subset $E$ of a domain $G$ in the complex plane is removable for analytic functions $f(z)$ defined in $G\setminus E$ and such that for any point $z_0\in E$ the real or imaginary part of $f(z)$ vanishes at $z_0$.  
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| Datum: | 2020 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2020
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/6046 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.537.38
We prove that each totally disconnected closed subset $E$ of a domain $G$ in the complex plane is removable for analytic functions $f(z)$ defined in $G\setminus E$ and such that for any point $z_0\in E$ the real or imaginary part of $f(z)$ vanishes at $z_0$.
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| DOI: | 10.37863/umzh.v72i3.6046 |