On the function approximation by trigonometric polynomials and the properties of families of function classes over harmonic intervals
The article is devoted to research on approximation theory. When approximating functions by trigonometric polynomials, the spectrum is chosen from various sets. In this paper, the spectrum consists of harmonic intervals. Devices, various processes, perception of the senses have a limited ra...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Academician Ye.A. Buketov Karaganda University
2023-09-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Online Access: | https://mathematics-vestnik.ksu.kz/apart/2023-111-3/15.pdf |
| _version_ | 1797636629696872448 |
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| author | G.A. Yessenbayeva A.N. Yesbayev N.K. Syzdykova M.A. Smirnova |
| author_facet | G.A. Yessenbayeva A.N. Yesbayev N.K. Syzdykova M.A. Smirnova |
| author_sort | G.A. Yessenbayeva |
| collection | DOAJ |
| description | The article is devoted to research on approximation theory. When approximating functions by trigonometric polynomials, the spectrum is chosen from various sets. In this paper, the spectrum consists of harmonic intervals. Devices, various processes, perception of the senses have a limited range. In the mathematical modeling of numerous practical problems and in the further study of such mathematical models, it is sufficient to find a solution in this range. It is possible to study such models to some extent with the help of harmonic intervals. To prove the main theorem, an auxiliary lemma was proved, and elements of the theory of approximations with respect to harmonic intervals were used. For the constructed families of function classes associated with the best approximations by trigonometric polynomials with a spectrum of harmonic intervals, their relationship with classical Besov spaces is shown |
| first_indexed | 2024-03-11T12:36:45Z |
| format | Article |
| id | doaj.art-95b0b6457e994772b3a23d8c725269cd |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-11T12:36:45Z |
| publishDate | 2023-09-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-95b0b6457e994772b3a23d8c725269cd2023-11-05T16:09:13ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112023-09-01111318119010.31489/2023M3/181-190On the function approximation by trigonometric polynomials and the properties of families of function classes over harmonic intervalsG.A. YessenbayevaA.N. YesbayevN.K. SyzdykovaM.A. Smirnova The article is devoted to research on approximation theory. When approximating functions by trigonometric polynomials, the spectrum is chosen from various sets. In this paper, the spectrum consists of harmonic intervals. Devices, various processes, perception of the senses have a limited range. In the mathematical modeling of numerous practical problems and in the further study of such mathematical models, it is sufficient to find a solution in this range. It is possible to study such models to some extent with the help of harmonic intervals. To prove the main theorem, an auxiliary lemma was proved, and elements of the theory of approximations with respect to harmonic intervals were used. For the constructed families of function classes associated with the best approximations by trigonometric polynomials with a spectrum of harmonic intervals, their relationship with classical Besov spaces is shownhttps://mathematics-vestnik.ksu.kz/apart/2023-111-3/15.pdf |
| spellingShingle | G.A. Yessenbayeva A.N. Yesbayev N.K. Syzdykova M.A. Smirnova On the function approximation by trigonometric polynomials and the properties of families of function classes over harmonic intervals Қарағанды университетінің хабаршысы. Математика сериясы |
| title | On the function approximation by trigonometric polynomials and the properties of families of function classes over harmonic intervals |
| title_full | On the function approximation by trigonometric polynomials and the properties of families of function classes over harmonic intervals |
| title_fullStr | On the function approximation by trigonometric polynomials and the properties of families of function classes over harmonic intervals |
| title_full_unstemmed | On the function approximation by trigonometric polynomials and the properties of families of function classes over harmonic intervals |
| title_short | On the function approximation by trigonometric polynomials and the properties of families of function classes over harmonic intervals |
| title_sort | on the function approximation by trigonometric polynomials and the properties of families of function classes over harmonic intervals |
| url | https://mathematics-vestnik.ksu.kz/apart/2023-111-3/15.pdf |
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