Approximation of classes of periodical functions of many variables
We study classes of periodic functions of several variables with bounded generalized derivative in the metric of the space Lp. We obtain order estimates of deviations of Fourier sums, which are constructed depending on the behavior of functions that define the operator of generalized differentiation...
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| Date: | 1992 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian |
| Published: |
Institute of Mathematics, NAS of Ukraine
1992
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7963 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512833495629824 |
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| author | Romanyuk , A. S. Романюк , А. С. |
| author_facet | Romanyuk , A. S. Романюк , А. С. |
| author_sort | Romanyuk , A. S. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-12-01T10:43:23Z |
| description | We study classes of periodic functions of several variables with bounded generalized derivative in the metric of the space Lp. We obtain order estimates of deviations of Fourier sums, which are constructed depending on the behavior of functions that define the operator of generalized differentiation. We find estimates of the Kolmogorov widths, which are realized by the Fourier sums that are constructed. |
| first_indexed | 2026-03-24T03:35:04Z |
| format | Article |
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| id | umjimathkievua-article-7963 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:35:04Z |
| publishDate | 1992 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/b2/5d78d2edcf58934448c738b7e051e0b2.pdf |
| spelling | umjimathkievua-article-79632023-12-01T10:43:23Z Approximation of classes of periodical functions of many variables О приближении классов периодических функций многих переменных Romanyuk , A. S. Романюк , А. С. We study classes of periodic functions of several variables with bounded generalized derivative in the metric of the space Lp. We obtain order estimates of deviations of Fourier sums, which are constructed depending on the behavior of functions that define the operator of generalized differentiation. We find estimates of the Kolmogorov widths, which are realized by the Fourier sums that are constructed. Изучаются классы периодических функций многих переменных с ограниченной обобщенной производной в метрике пространства Lp. Получены порядковые оценки уклонений сумм Фурье, построенных в зависимости от поведения функций, определяющих оператор обобщенного дифференцирования. Найдены оценки колмогорозских поперечников, которые реализуются построенными суммами Фурье. Вивчаються класи періодичних функцій багатьох змінних з обмеженою узагальненою похідною в метриці простору Lp. Одержані порядкові оцінки відхилень сум Фур’є, побудованих в залежності від поведінки функцій, які визначають оператор узагальненого диференціювання. Знайдені оцінки колмогорівських поперечників, які реалізуються побудованими сумами Фур’є. Institute of Mathematics, NAS of Ukraine 1992-05-26 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/7963 Ukrains’kyi Matematychnyi Zhurnal; Vol. 44 No. 5 (1992); 662-672 Український математичний журнал; Том 44 № 5 (1992); 662-672 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/7963/9556 |
| spellingShingle | Romanyuk , A. S. Романюк , А. С. Approximation of classes of periodical functions of many variables |
| title | Approximation of classes of periodical functions of many variables |
| title_alt | О приближении классов периодических функций многих переменных |
| title_full | Approximation of classes of periodical functions of many variables |
| title_fullStr | Approximation of classes of periodical functions of many variables |
| title_full_unstemmed | Approximation of classes of periodical functions of many variables |
| title_short | Approximation of classes of periodical functions of many variables |
| title_sort | approximation of classes of periodical functions of many variables |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7963 |
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