Approximative characteristics of the Nikol’skii – Besov classes of functions $S_{1, θ}^r B(\mathbb{R}^d)$
UDC 517.51 We establish the exact-order estimates for the approximation of the classes $S^{\boldsymbol{r}}_{1,\theta}B \left(\mathbb{R}^d\right)$ by entire functions of exponential type with supports of their Fourier transforms lying in a step hyperbolic cross. The error of approximation is estima...
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| Datum: | 2026 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/1523 |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860507317750988800 |
|---|---|
| author | Radchenko, O. Ya. Yanchenko, S. Ya. Радченко, О. Я. Янченко, С. Я. |
| author_facet | Radchenko, O. Ya. Yanchenko, S. Ya. Радченко, О. Я. Янченко, С. Я. |
| author_sort | Radchenko, O. Ya. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-02-09T14:34:17Z |
| description | UDC 517.51
We establish the exact-order estimates for the approximation of the classes $S^{\boldsymbol{r}}_{1,\theta}B \left(\mathbb{R}^d\right)$ by entire functions of exponential type with supports of their Fourier transforms lying in a step hyperbolic cross.
The error of approximation is estimated in the metric of the Lebesgue space $L_q\left(\mathbb{R}^d\right),\; 1 < q \leq \infty.$ |
| doi_str_mv | 10.3842/umzh.v71i10.1523 |
| first_indexed | 2026-03-24T02:07:24Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-1523 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian |
| last_indexed | 2026-03-24T02:07:24Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/a9/4d7d83f78f453036f94714b005ee5ea9 |
| spelling | umjimathkievua-article-15232026-02-09T14:34:17Z Approximative characteristics of the Nikol’skii – Besov classes of functions $S_{1, θ}^r B(\mathbb{R}^d)$ Апроксимативні характеристики класів функцій Нікольського – Бєсова $S_{1, θ}^r B(\mathbb{R}^d)$ Radchenko, O. Ya. Yanchenko, S. Ya. Радченко, О. Я. Янченко, С. Я. UDC 517.51 We establish the exact-order estimates for the approximation of the classes $S^{\boldsymbol{r}}_{1,\theta}B \left(\mathbb{R}^d\right)$ by entire functions of exponential type with supports of their Fourier transforms lying in a step hyperbolic cross. The error of approximation is estimated in the metric of the Lebesgue space $L_q\left(\mathbb{R}^d\right),\; 1 < q \leq \infty.$ УДК 517.51 Одержано точні за порядком оцінки наближення класів функцій $S^{\boldsymbol{r}}_{1,\theta}B\left(\mathbb{R}^d\right)$ за допомогою цілих функцій експоненціального типу з носіями їхнього перетворення Фур'є у східчастому гіперболічному хресті. Похибку наближення оцінено в метриці простору Лебега $L_q\left(\mathbb{R}^d\right),\; 1 < q \leq \infty.$ Institute of Mathematics, NAS of Ukraine 2026-02-09 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/1523 10.3842/umzh.v71i10.1523 Ukrains’kyi Matematychnyi Zhurnal; Vol. 71 No. 10 (2019); 1405-1421 Український математичний журнал; Том 71 № 10 (2019); 1405-1421 1027-3190 uk https://umj.imath.kiev.ua/index.php/umj/article/view/1523/506 Copyright (c) 2019 Radchenko O. Ya.; Yanchenko S. Ya. |
| spellingShingle | Radchenko, O. Ya. Yanchenko, S. Ya. Радченко, О. Я. Янченко, С. Я. Approximative characteristics of the Nikol’skii – Besov classes of functions $S_{1, θ}^r B(\mathbb{R}^d)$ |
| title | Approximative characteristics of the Nikol’skii – Besov
classes of functions $S_{1, θ}^r B(\mathbb{R}^d)$ |
| title_alt | Апроксимативні характеристики класів функцій
Нікольського – Бєсова $S_{1, θ}^r B(\mathbb{R}^d)$ |
| title_full | Approximative characteristics of the Nikol’skii – Besov
classes of functions $S_{1, θ}^r B(\mathbb{R}^d)$ |
| title_fullStr | Approximative characteristics of the Nikol’skii – Besov
classes of functions $S_{1, θ}^r B(\mathbb{R}^d)$ |
| title_full_unstemmed | Approximative characteristics of the Nikol’skii – Besov
classes of functions $S_{1, θ}^r B(\mathbb{R}^d)$ |
| title_short | Approximative characteristics of the Nikol’skii – Besov
classes of functions $S_{1, θ}^r B(\mathbb{R}^d)$ |
| title_sort | approximative characteristics of the nikol’skii – besov
classes of functions $s_{1, θ}^r b(\mathbb{r}^d)$ |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/1523 |
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