On the best polynomial approximation of entire transcendental functions of generalized order
We prove a Hadamard-type theorem which connects the generalized order of growth $\rho^*_f(\alpha, \beta)$ of entire transcendental function $f$ with coefficients of its expansion into the Faber series. The theorem is an original extension of a certain result by S. K. Balashov to the case of finite...
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| Datum: | 2008 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2008
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3219 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | We prove a Hadamard-type theorem which connects the generalized order of growth $\rho^*_f(\alpha, \beta)$ of entire transcendental function $f$ with coefficients of its expansion into the Faber series. The theorem is an original extension of a certain result by S. K. Balashov to the case of finite simply connected domain $G$ with the boundary $\gamma$ belonging to the S. Ya. Al'per class $\Lambda^*.$
This enables us to obtain boundary equalities that connect $\rho^*_f(\alpha, \beta)$ with the sequence of the best polynomial approximations of $f$ in some Banach spaces of functions analytic in $G$.
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