Conditions of integration of multiple trigonometric series
Sufficient conditions (the Boas-Telyakovskii conditions) on the coefficients of multiple trigonometric series are found that guarantee integrability of the sums of these series. Under these conditions, estimates are obtained for integrals of the moduli of the functions defined by multiple trigonomet...
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| Date: | 1992 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian |
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Institute of Mathematics, NAS of Ukraine
1992
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8103 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512904724348928 |
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| author | Zaderei, P. V. Задерей, П. В. |
| author_facet | Zaderei, P. V. Задерей, П. В. |
| author_sort | Zaderei, P. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-01-31T10:37:52Z |
| description | Sufficient conditions (the Boas-Telyakovskii conditions) on the coefficients of multiple trigonometric series are found that guarantee integrability of the sums of these series. Under these conditions, estimates are obtained for integrals of the moduli of the functions defined by multiple trigonometric series. In addition, the Boas-Telyakovskii conditions are compared with previously known conditions. It is shown that the Boas-Telyakovskii conditions are the most general ones.
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| first_indexed | 2026-03-24T03:36:12Z |
| format | Article |
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| id | umjimathkievua-article-8103 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:36:12Z |
| publishDate | 1992 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/28/d71df598e4b9bfed71b55053c027e728.pdf |
| spelling | umjimathkievua-article-81032024-01-31T10:37:52Z Conditions of integration of multiple trigonometric series Об условиях интегрируемости кратных тригонометрических рядов Zaderei, P. V. Задерей, П. В. Sufficient conditions (the Boas-Telyakovskii conditions) on the coefficients of multiple trigonometric series are found that guarantee integrability of the sums of these series. Under these conditions, estimates are obtained for integrals of the moduli of the functions defined by multiple trigonometric series. In addition, the Boas-Telyakovskii conditions are compared with previously known conditions. It is shown that the Boas-Telyakovskii conditions are the most general ones. Найдены достаточные условия (условия Боаса — Теляковского) на коэффициенты кратных тригонометрических рядов, обеспечивающие интегрируемость сумм рассматриваемых рядов. При этих условиях получены оценки интегралов от модулей функций, заданных кратными тригонометрическими рядами. Дано также сравнение условий Боаса—Теляковского с ранее известными условиями. Доказано, что условия Боаса—Теляковского являются наиболее общими. Знайдені достатні умови (умови Боаса — Теляковського) на коефіцієнти кратних тригонометричних рядів, які забезпечують інтегровність сум розглядуваних рядів. При цих умовах одержані оцінки інтегралів від модулів функцій, заданих кратними тригонометричними рядами. Дано також порівняння умов Боаса—Теляковського з раніше відомими умовами,. Доведено, що умови Боаса—Теляковського є найбільш загальними. Institute of Mathematics, NAS of Ukraine 1992-04-02 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/8103 Ukrains’kyi Matematychnyi Zhurnal; Vol. 44 No. 3 (1992); 340-365 Український математичний журнал; Том 44 № 3 (1992); 340-365 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/8103/9634 Copyright (c) 1992 P. V. Zaderei |
| spellingShingle | Zaderei, P. V. Задерей, П. В. Conditions of integration of multiple trigonometric series |
| title | Conditions of integration of multiple trigonometric series |
| title_alt | Об условиях интегрируемости кратных тригонометрических рядов |
| title_full | Conditions of integration of multiple trigonometric series |
| title_fullStr | Conditions of integration of multiple trigonometric series |
| title_full_unstemmed | Conditions of integration of multiple trigonometric series |
| title_short | Conditions of integration of multiple trigonometric series |
| title_sort | conditions of integration of multiple trigonometric series |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8103 |
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