Fourier Series Approximation in Besov Spaces
Defined on the top of classical Lp-spaces, the Besov spaces of periodic functions are good at encoding the smoothness properties of their elements. These spaces are also characterized in terms of summability conditions on the coefficients in trigonometric series expansions of their elements. In this...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/4250869 |
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| _version_ | 1832554123759714304 |
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| author | Birendra Singh Uaday Singh |
| author_facet | Birendra Singh Uaday Singh |
| author_sort | Birendra Singh |
| collection | DOAJ |
| description | Defined on the top of classical Lp-spaces, the Besov spaces of periodic functions are good at encoding the smoothness properties of their elements. These spaces are also characterized in terms of summability conditions on the coefficients in trigonometric series expansions of their elements. In this paper, we study the approximation properties of 2π-periodic functions in a Besov space under a norm involving the seminorm associated with the space. To achieve our results, we use a summability method presented by a lower triangular matrix with monotonic rows. |
| format | Article |
| id | doaj-art-ea5f1328f670461a85d0a0945fc31203 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-ea5f1328f670461a85d0a0945fc312032025-02-03T05:52:24ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/4250869Fourier Series Approximation in Besov SpacesBirendra Singh0Uaday Singh1Department of MathematicsDepartment of MathematicsDefined on the top of classical Lp-spaces, the Besov spaces of periodic functions are good at encoding the smoothness properties of their elements. These spaces are also characterized in terms of summability conditions on the coefficients in trigonometric series expansions of their elements. In this paper, we study the approximation properties of 2π-periodic functions in a Besov space under a norm involving the seminorm associated with the space. To achieve our results, we use a summability method presented by a lower triangular matrix with monotonic rows.http://dx.doi.org/10.1155/2023/4250869 |
| spellingShingle | Birendra Singh Uaday Singh Fourier Series Approximation in Besov Spaces Journal of Mathematics |
| title | Fourier Series Approximation in Besov Spaces |
| title_full | Fourier Series Approximation in Besov Spaces |
| title_fullStr | Fourier Series Approximation in Besov Spaces |
| title_full_unstemmed | Fourier Series Approximation in Besov Spaces |
| title_short | Fourier Series Approximation in Besov Spaces |
| title_sort | fourier series approximation in besov spaces |
| url | http://dx.doi.org/10.1155/2023/4250869 |
| work_keys_str_mv | AT birendrasingh fourierseriesapproximationinbesovspaces AT uadaysingh fourierseriesapproximationinbesovspaces |