On the strong summability of the Fourier–Walsh series in the Besov space
UDC 517.5 The Fourier–Walsh series of even continuous functions may be divergent at some points. Moreover, among integrable functions, there are functions such that their Fourier–Walsh series diverge everywhere on $[0,1)$.  In this connection, it becomes necess...
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| Дата: | 2025 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
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Institute of Mathematics, NAS of Ukraine
2025
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/7577 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512687249686528 |
|---|---|
| author | Igenberlina, A. Keulimzhayeva, Zh. Igenberlina, A. Keulimzhayeva, Zh. |
| author_facet | Igenberlina, A. Keulimzhayeva, Zh. Igenberlina, A. Keulimzhayeva, Zh. |
| author_sort | Igenberlina, A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-04-16T12:01:16Z |
| description | UDC 517.5
The Fourier–Walsh series of even continuous functions may be divergent at some points. Moreover, among integrable functions, there are functions such that their Fourier–Walsh series diverge everywhere on $[0,1)$.  In this connection, it becomes necessary to consider various summation methods that would allow us to restore the function according to its Fourier–Walsh series. We also investigate the Besov space on a dyadic group in terms of strong summability.  Finally, we present  necessary information about the Fourier–Walsh transform. |
| doi_str_mv | 10.3842/umzh.v76i9.7577 |
| first_indexed | 2026-03-24T03:32:45Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7577 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:45Z |
| publishDate | 2025 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-75772025-04-16T12:01:16Z On the strong summability of the Fourier–Walsh series in the Besov space On the strong summability of the Fourier–Walsh series in the Besov space Igenberlina, A. Keulimzhayeva, Zh. Igenberlina, A. Keulimzhayeva, Zh. Walsh functions, dyadic group, Fourier transform, Besov space UDC 517.5 The Fourier–Walsh series of even continuous functions may be divergent at some points. Moreover, among integrable functions, there are functions such that their Fourier–Walsh series diverge everywhere on $[0,1)$.  In this connection, it becomes necessary to consider various summation methods that would allow us to restore the function according to its Fourier–Walsh series. We also investigate the Besov space on a dyadic group in terms of strong summability.  Finally, we present  necessary information about the Fourier–Walsh transform. УДК 517.5 Про сильну сумовність ряду Фур'є–Уолша в просторі Бєсова Ряди Фур'є–Уолша парних неперервних функцій можуть бути розбіжними в деяких точках, а серед інтегровних функцій є такі, що їх ряди Фур'є–Уолша розбігаються скрізь на $[0,1)$. У зв'язку з цим виникає необхідність розглянути різні методи підсумовування, які б дозволили відновити функцію за допомогою її ряду Фур'є–Уолша. Крім того, досліджено простір Бєсова на діадній групі з точки зору сильної сумовності. Насамкінець наведено необхідну інформацію про перетворення Фур'є–Уолша. Institute of Mathematics, NAS of Ukraine 2025-04-16 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7577 10.3842/umzh.v76i9.7577 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 9 (2024); 1304 - 1315 Український математичний журнал; Том 76 № 9 (2024); 1304 - 1315 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7577/10164 Copyright (c) 2024 Zhanar Keulimzhayeva |
| spellingShingle | Igenberlina, A. Keulimzhayeva, Zh. Igenberlina, A. Keulimzhayeva, Zh. On the strong summability of the Fourier–Walsh series in the Besov space |
| title | On the strong summability of the Fourier–Walsh series in the Besov space |
| title_alt | On the strong summability of the Fourier–Walsh series in the Besov space |
| title_full | On the strong summability of the Fourier–Walsh series in the Besov space |
| title_fullStr | On the strong summability of the Fourier–Walsh series in the Besov space |
| title_full_unstemmed | On the strong summability of the Fourier–Walsh series in the Besov space |
| title_short | On the strong summability of the Fourier–Walsh series in the Besov space |
| title_sort | on the strong summability of the fourier–walsh series in the besov space |
| topic_facet | Walsh functions dyadic group Fourier transform Besov space |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7577 |
| work_keys_str_mv | AT igenberlinaa onthestrongsummabilityofthefourierwalshseriesinthebesovspace AT keulimzhayevazh onthestrongsummabilityofthefourierwalshseriesinthebesovspace AT igenberlinaa onthestrongsummabilityofthefourierwalshseriesinthebesovspace AT keulimzhayevazh onthestrongsummabilityofthefourierwalshseriesinthebesovspace |