Coefficients of multiple Fourier-Haar series and variational modulus of continuity
In this paper, we introduce the concept of a variational modulus of continuity for functions of several variables, give an estimate for the sum of the coefficients of a multiple Fourier-Haar series in terms of the variational modulus of continuity, and prove theorems of absolute convergence of seri...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2023-12-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Subjects: | |
| Online Access: | https://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/602 |
| _version_ | 1797372706718482432 |
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| author | T.B. Akhazhanov N.А. Bokayev D.T. Matin T. Aktosun |
| author_facet | T.B. Akhazhanov N.А. Bokayev D.T. Matin T. Aktosun |
| author_sort | T.B. Akhazhanov |
| collection | DOAJ |
| description |
In this paper, we introduce the concept of a variational modulus of continuity for functions of several variables, give an estimate for the sum of the coefficients of a multiple Fourier-Haar series in terms of the variational modulus of continuity, and prove theorems of absolute convergence of series composed of the coefficients of multiple Fourier-Haar series. In this paper, we study the issue of the absolute convergence for multiple series composed of the Fourier-Haar coefficients of functions of several variables of bounded p-variation. We estimate the coefficients of a multiple Fourier-Haar series in terms of the variational modulus of continuity and prove the sufficiency theorem for the condition for the absolute convergence of series composed of the Fourier-Haar coefficients of the considered function class. This paper researches the question: under what conditions, imposed on the variational modulus of continuity of the fractional order of several variables functions, there is the absolute convergence for series composed of the coefficients of multiple Fourier-Haar series.
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| first_indexed | 2024-03-08T18:39:41Z |
| format | Article |
| id | doaj.art-2e92a178ec3b436392b65444690754ba |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:39:41Z |
| publishDate | 2023-12-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-2e92a178ec3b436392b65444690754ba2023-12-29T09:21:06ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112023-12-01112410.31489/2023m4/21-29602Coefficients of multiple Fourier-Haar series and variational modulus of continuityT.B. AkhazhanovN.А. BokayevD.T. MatinT. Aktosun In this paper, we introduce the concept of a variational modulus of continuity for functions of several variables, give an estimate for the sum of the coefficients of a multiple Fourier-Haar series in terms of the variational modulus of continuity, and prove theorems of absolute convergence of series composed of the coefficients of multiple Fourier-Haar series. In this paper, we study the issue of the absolute convergence for multiple series composed of the Fourier-Haar coefficients of functions of several variables of bounded p-variation. We estimate the coefficients of a multiple Fourier-Haar series in terms of the variational modulus of continuity and prove the sufficiency theorem for the condition for the absolute convergence of series composed of the Fourier-Haar coefficients of the considered function class. This paper researches the question: under what conditions, imposed on the variational modulus of continuity of the fractional order of several variables functions, there is the absolute convergence for series composed of the coefficients of multiple Fourier-Haar series. https://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/602Fourier-Haar seriesvariational modulus of continuitycoefficients of multiple Fourier-Haar series |
| spellingShingle | T.B. Akhazhanov N.А. Bokayev D.T. Matin T. Aktosun Coefficients of multiple Fourier-Haar series and variational modulus of continuity Қарағанды университетінің хабаршысы. Математика сериясы Fourier-Haar series variational modulus of continuity coefficients of multiple Fourier-Haar series |
| title | Coefficients of multiple Fourier-Haar series and variational modulus of continuity |
| title_full | Coefficients of multiple Fourier-Haar series and variational modulus of continuity |
| title_fullStr | Coefficients of multiple Fourier-Haar series and variational modulus of continuity |
| title_full_unstemmed | Coefficients of multiple Fourier-Haar series and variational modulus of continuity |
| title_short | Coefficients of multiple Fourier-Haar series and variational modulus of continuity |
| title_sort | coefficients of multiple fourier haar series and variational modulus of continuity |
| topic | Fourier-Haar series variational modulus of continuity coefficients of multiple Fourier-Haar series |
| url | https://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/602 |
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