Fourier coefficients of functions from the classes $B$ and $C$. Parseval equality for the class $C$ or for the Fourier-Stieltjes series
We study restrictions that should be imposed on the numbers sequences $\{α_n\}$ and $\{Β_n\}$ in order to guarantee that the series $\sum\nolimits_{n = 1}^\infty {a_n } \cos nx$ and $\sum\nolimits_{n = 1}^\infty {b_n } \sin nx$ do not belong to the classes $B$ or $C$ for any {a n } and {b n }...
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| Datum: | 1993 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1993
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5951 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512172817252352 |
|---|---|
| author | Konyushkov, A. A. Конюшков, А. А. Конюшков, А. А. |
| author_facet | Konyushkov, A. A. Конюшков, А. А. Конюшков, А. А. |
| author_sort | Konyushkov, A. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:21:43Z |
| description | We study restrictions that should be imposed on the numbers sequences $\{α_n\}$ and $\{Β_n\}$ in order to guarantee that the series $\sum\nolimits_{n = 1}^\infty {a_n } \cos nx$ and $\sum\nolimits_{n = 1}^\infty {b_n } \sin nx$ do not belong to the classes $B$ or $C$ for any {a n } and {b n } such that $a_n ≥ α_n, b_n ≥ Β_n,\; n = 1, 2$. |
| first_indexed | 2026-03-24T03:24:34Z |
| format | Article |
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| id | umjimathkievua-article-5951 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:24:34Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/63/0669ff6b02347a6262fa8b6a47f86563.pdf |
| spelling | umjimathkievua-article-59512020-03-19T09:21:43Z Fourier coefficients of functions from the classes $B$ and $C$. Parseval equality for the class $C$ or for the Fourier-Stieltjes series О коэффициентах Фурье функций классов $B$ и $C$ и равенстве Парсеваля для класса $C$ или для рядов Фурье - Стилтьеса Konyushkov, A. A. Конюшков, А. А. Конюшков, А. А. We study restrictions that should be imposed on the numbers sequences $\{α_n\}$ and $\{Β_n\}$ in order to guarantee that the series $\sum\nolimits_{n = 1}^\infty {a_n } \cos nx$ and $\sum\nolimits_{n = 1}^\infty {b_n } \sin nx$ do not belong to the classes $B$ or $C$ for any {a n } and {b n } such that $a_n ≥ α_n, b_n ≥ Β_n,\; n = 1, 2$. Вивчається питання про обмеження на послідовності чисел $\{α_n\}$, $\{Β_n\}$, при яких для будь-яких $\{α_n\}$, $\{Β_n\}$ з $a_n ≥ α_n, b_n ≥ Β_n,\; n = 1, 2$. ряди $\sum\nolimits_{n = 1}^\infty {a_n } \cos nx$, $\sum\nolimits_{n = 1}^\infty {b_n } \sin nx$ не належать класу $B$ або $C$ . Institute of Mathematics, NAS of Ukraine 1993-10-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5951 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 10 (1993); 1455–1460 Український математичний журнал; Том 45 № 10 (1993); 1455–1460 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5951/8585 https://umj.imath.kiev.ua/index.php/umj/article/view/5951/8586 Copyright (c) 1993 Konyushkov A. A. |
| spellingShingle | Konyushkov, A. A. Конюшков, А. А. Конюшков, А. А. Fourier coefficients of functions from the classes $B$ and $C$. Parseval equality for the class $C$ or for the Fourier-Stieltjes series |
| title | Fourier coefficients of functions from the classes $B$ and $C$. Parseval equality for the class $C$ or for the Fourier-Stieltjes series |
| title_alt | О коэффициентах Фурье функций классов $B$ и $C$ и равенстве Парсеваля для класса $C$ или для рядов Фурье - Стилтьеса |
| title_full | Fourier coefficients of functions from the classes $B$ and $C$. Parseval equality for the class $C$ or for the Fourier-Stieltjes series |
| title_fullStr | Fourier coefficients of functions from the classes $B$ and $C$. Parseval equality for the class $C$ or for the Fourier-Stieltjes series |
| title_full_unstemmed | Fourier coefficients of functions from the classes $B$ and $C$. Parseval equality for the class $C$ or for the Fourier-Stieltjes series |
| title_short | Fourier coefficients of functions from the classes $B$ and $C$. Parseval equality for the class $C$ or for the Fourier-Stieltjes series |
| title_sort | fourier coefficients of functions from the classes $b$ and $c$. parseval equality for the class $c$ or for the fourier-stieltjes series |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5951 |
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