On the Best Polynomial Approximations of Entire Transcendental Functions of Many Complex Variables in Some Banach Spaces
For the entire transcendental functions $f$ of many complex variables $m (m ≥ 2)$ of finite generalized order of growth $ρ_m (f; α, β)$, we obtain the limiting relations between the indicated characteristic of growth and the sequences of best polynomial approximations of $f$ in the Hardy Banach spac...
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| Datum: | 2014 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2014
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/2249 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | For the entire transcendental functions $f$ of many complex variables $m (m ≥ 2)$ of finite generalized order of growth $ρ_m (f; α, β)$, we obtain the limiting relations between the indicated characteristic of growth and the sequences of best polynomial approximations of $f$ in the Hardy Banach spaces $H q (U^m )$ and in the Banach spaces $Bm(p, q, ⋋)$ studied by Gvaradze. The presented results are extensions of the corresponding assertions made by Varga, Batyrev, Shah, Reddy, Ibragimov, and Shikhaliev to the multidimensional case. |
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