Approximation of the Nikol'skii-Besov functional classes by entire functions of a special form
We establish the exact-order estimates for the approximation of functions from the Nikol'skii-Besov classes $S^{\boldsymbol{r}}_{1,\theta}B(\mathbb{R}^d)$, $d\geq 1$, by entire functions of exponential type with some restrictions for their spectrum. The error of the approximation is estimated i...
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2020-06-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
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| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/3895 |
| _version_ | 1797205829702647808 |
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| author | S.Ya. Yanchenko |
| author_facet | S.Ya. Yanchenko |
| author_sort | S.Ya. Yanchenko |
| collection | DOAJ |
| description | We establish the exact-order estimates for the approximation of functions from the Nikol'skii-Besov classes $S^{\boldsymbol{r}}_{1,\theta}B(\mathbb{R}^d)$, $d\geq 1$, by entire functions of exponential type with some restrictions for their spectrum. The error of the approximation is estimated in the metric of the Lebesgue space $L_{\infty}(\mathbb{R}^d)$. |
| first_indexed | 2024-04-24T08:57:21Z |
| format | Article |
| id | doaj.art-375f5082b8284bc2bf1470320278af71 |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-04-24T08:57:21Z |
| publishDate | 2020-06-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-375f5082b8284bc2bf1470320278af712024-04-16T07:00:37ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102020-06-0112114815610.15330/cmp.12.1.148-1563387Approximation of the Nikol'skii-Besov functional classes by entire functions of a special formS.Ya. Yanchenko0https://orcid.org/0000-0003-4906-3806Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereschenkivska str., 01024, Kyiv, UkraineWe establish the exact-order estimates for the approximation of functions from the Nikol'skii-Besov classes $S^{\boldsymbol{r}}_{1,\theta}B(\mathbb{R}^d)$, $d\geq 1$, by entire functions of exponential type with some restrictions for their spectrum. The error of the approximation is estimated in the metric of the Lebesgue space $L_{\infty}(\mathbb{R}^d)$.https://journals.pnu.edu.ua/index.php/cmp/article/view/3895nikol'skii-besov classesentire functions of exponential typefourier transform |
| spellingShingle | S.Ya. Yanchenko Approximation of the Nikol'skii-Besov functional classes by entire functions of a special form Karpatsʹkì Matematičnì Publìkacìï nikol'skii-besov classes entire functions of exponential type fourier transform |
| title | Approximation of the Nikol'skii-Besov functional classes by entire functions of a special form |
| title_full | Approximation of the Nikol'skii-Besov functional classes by entire functions of a special form |
| title_fullStr | Approximation of the Nikol'skii-Besov functional classes by entire functions of a special form |
| title_full_unstemmed | Approximation of the Nikol'skii-Besov functional classes by entire functions of a special form |
| title_short | Approximation of the Nikol'skii-Besov functional classes by entire functions of a special form |
| title_sort | approximation of the nikol skii besov functional classes by entire functions of a special form |
| topic | nikol'skii-besov classes entire functions of exponential type fourier transform |
| url | https://journals.pnu.edu.ua/index.php/cmp/article/view/3895 |
| work_keys_str_mv | AT syayanchenko approximationofthenikolskiibesovfunctionalclassesbyentirefunctionsofaspecialform |