On the best polynomial approximation of entire transcendental functions in Banach spaces. II
We study the behavior of the best approximations $E_n(f)_{E′_p}$ of entire transcendental functions $f(z)$ of the order $ρ = 0$ by polynomials of at most $n$ th degree in the metric of the space $E′_p(Ω),\, p ≥ 1$. In particular, we describe the relationship between the best approximations $E_n(f...
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| Date: | 1994 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
1994
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5609 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511838946459648 |
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| author | Vakarchuk, S. B. Вакарчук, С. Б. Вакарчук, С. Б. |
| author_facet | Vakarchuk, S. B. Вакарчук, С. Б. Вакарчук, С. Б. |
| author_sort | Vakarchuk, S. B. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:14:35Z |
| description | We study the behavior of the best approximations $E_n(f)_{E′_p}$ of entire transcendental functions $f(z)$ of the order $ρ = 0$ by polynomials of at most $n$ th degree in the metric of the space $E′_p(Ω),\, p ≥ 1$. In particular, we describe the relationship between the best approximations $E_n(f)E′_p$ and the logarithmic order $ρ_L$ and type $σ_L$ of the function $f(z)$. |
| first_indexed | 2026-03-24T03:19:16Z |
| format | Article |
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| id | umjimathkievua-article-5609 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:19:16Z |
| publishDate | 1994 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/0c/d38d8d0b68bc80da485caa162e9bf60c.pdf |
| spelling | umjimathkievua-article-56092020-03-19T09:14:35Z On the best polynomial approximation of entire transcendental functions in Banach spaces. II О наилучшем полиномиальном приближении целых трансцендентных функций в некоторых банаховых пространствах. II Vakarchuk, S. B. Вакарчук, С. Б. Вакарчук, С. Б. We study the behavior of the best approximations $E_n(f)_{E′_p}$ of entire transcendental functions $f(z)$ of the order $ρ = 0$ by polynomials of at most $n$ th degree in the metric of the space $E′_p(Ω),\, p ≥ 1$. In particular, we describe the relationship between the best approximations $E_n(f)E′_p$ and the logarithmic order $ρ_L$ and type $σ_L$ of the function $f(z)$. Для цілих трансцендентних функцій $f(z)$, що мають порядок $ρ = 0$, у метриці простору $E′_p(Ω),\, p ≥ 1$, розглянуто питання поведінки найкращих наближень $E_n(f)_{E′_p}$- поліномами степеня $ ≥ n$. Зокрема, встановлені співвідношення, що зв’язують логарифмічний порядок $ρ_L$ і $σ_L$ і тип функції $f(z)$ з $E_n(f)E′_p$. Institute of Mathematics, NAS of Ukraine 1994-10-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5609 Ukrains’kyi Matematychnyi Zhurnal; Vol. 46 No. 10 (1994); 1318–1322 Український математичний журнал; Том 46 № 10 (1994); 1318–1322 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5609/7903 https://umj.imath.kiev.ua/index.php/umj/article/view/5609/7904 Copyright (c) 1994 Vakarchuk S. B. |
| spellingShingle | Vakarchuk, S. B. Вакарчук, С. Б. Вакарчук, С. Б. On the best polynomial approximation of entire transcendental functions in Banach spaces. II |
| title | On the best polynomial approximation of entire transcendental functions in Banach spaces. II |
| title_alt | О наилучшем полиномиальном приближении целых трансцендентных функций в некоторых банаховых пространствах. II |
| title_full | On the best polynomial approximation of entire transcendental functions in Banach spaces. II |
| title_fullStr | On the best polynomial approximation of entire transcendental functions in Banach spaces. II |
| title_full_unstemmed | On the best polynomial approximation of entire transcendental functions in Banach spaces. II |
| title_short | On the best polynomial approximation of entire transcendental functions in Banach spaces. II |
| title_sort | on the best polynomial approximation of entire transcendental functions in banach spaces. ii |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5609 |
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