Approximation of holomorphic functions by Cesàro means
UDC 517.5 For the Lipschitz class of functions holomorphic in the disc, we present a constructive characterization of this class in terms of Cesaro’s means of order $\alpha \ge 2$ of the Taylor series. We solve the problem of exact upper bound for the deviations of Cesaro’s means of order $\alpha \g...
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| Datum: | 2022 |
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| Hauptverfasser: | , , , , , , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2022
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7143 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.5
For the Lipschitz class of functions holomorphic in the disc, we present a constructive characterization of this class in terms of Cesaro’s means of order $\alpha \ge 2$ of the Taylor series. We solve the problem of exact upper bound for the deviations of Cesaro’s means of order $\alpha \ge 2$ as well as for the deviations of Riesz’s means of order 2 of the Taylor series in the class of functions holomorphic in the disc and having a bounded derivative.
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| DOI: | 10.37863/umzh.v74i5.7143 |