Approximation of the $\bar {\Psi}$ -integrals of functions defined on the real axis by Fourier operators
We find asymptotic formulas for the least upper bounds of the deviations of Fourier operators on classes of functions locally summable on the entire real axis and defined by $\bar {\Psi}$-integrals. On these classes, we also obtain asymptotic equalities for the upper bounds of functionals that chara...
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| Date: | 2004 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
2004
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3812 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860509943735517184 |
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| author | Sokolenko, I. V. Stepanets, O. I. Соколенко, І. В. Степанець, О. І. |
| author_facet | Sokolenko, I. V. Stepanets, O. I. Соколенко, І. В. Степанець, О. І. |
| author_sort | Sokolenko, I. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:11:04Z |
| description | We find asymptotic formulas for the least upper bounds of the deviations of Fourier operators on classes of functions locally summable on the entire real axis and defined by $\bar {\Psi}$-integrals. On these classes, we also obtain asymptotic equalities for the upper bounds of functionals that characterize the simultaneous approximation of several functions. |
| first_indexed | 2026-03-24T02:49:08Z |
| format | Article |
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| id | umjimathkievua-article-3812 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:49:08Z |
| publishDate | 2004 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/a3/b94454d66df009b22d6187730721f0a3.pdf |
| spelling | umjimathkievua-article-38122020-03-18T20:11:04Z Approximation of the $\bar {\Psi}$ -integrals of functions defined on the real axis by Fourier operators Наближення операторами Фур'є $\bar {\Psi}$-інтегралів функцій, заданих на дійсній осі Sokolenko, I. V. Stepanets, O. I. Соколенко, І. В. Степанець, О. І. We find asymptotic formulas for the least upper bounds of the deviations of Fourier operators on classes of functions locally summable on the entire real axis and defined by $\bar {\Psi}$-integrals. On these classes, we also obtain asymptotic equalities for the upper bounds of functionals that characterize the simultaneous approximation of several functions. Знайдено асимптотичні формули для точних рерхиіх меж відхилень операторів Фур'є на класах локально сумовиих на всій дійсній осі функцій, що задаються $\bar {\Psi}$-інтегралами. На таких класах одержано також асимптотичні рівності для верхніх меж функціоналів, що характеризують одночасне наближення кількох функцій. Institute of Mathematics, NAS of Ukraine 2004-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3812 Ukrains’kyi Matematychnyi Zhurnal; Vol. 56 No. 7 (2004); 960–965 Український математичний журнал; Том 56 № 7 (2004); 960–965 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/3812/4344 https://umj.imath.kiev.ua/index.php/umj/article/view/3812/4345 Copyright (c) 2004 Sokolenko I. V.; Stepanets O. I. |
| spellingShingle | Sokolenko, I. V. Stepanets, O. I. Соколенко, І. В. Степанець, О. І. Approximation of the $\bar {\Psi}$ -integrals of functions defined on the real axis by Fourier operators |
| title | Approximation of the $\bar {\Psi}$
-integrals of functions defined on the real axis by Fourier operators |
| title_alt | Наближення операторами Фур'є $\bar {\Psi}$-інтегралів функцій, заданих на дійсній осі |
| title_full | Approximation of the $\bar {\Psi}$
-integrals of functions defined on the real axis by Fourier operators |
| title_fullStr | Approximation of the $\bar {\Psi}$
-integrals of functions defined on the real axis by Fourier operators |
| title_full_unstemmed | Approximation of the $\bar {\Psi}$
-integrals of functions defined on the real axis by Fourier operators |
| title_short | Approximation of the $\bar {\Psi}$
-integrals of functions defined on the real axis by Fourier operators |
| title_sort | approximation of the $\bar {\psi}$
-integrals of functions defined on the real axis by fourier operators |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3812 |
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