More on fast decreasing trigonometric polynomials
In a recent paper, for a fixed $m\in\mathbb N$, we introduced trigonometric polynomials $$ L_n(x):=\frac1{h^m}\underbrace{\int_{-h/2}^{h/2}\dots\int_{-h/2}^{h/2}}_{m\,\text{times}}J_n(x+t_1+\cdots+t_m)\,dt_1\cdots\,dt_m, $$ where $J_n$ is a Jackson-type kernel. In the current paper we show that...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Oles Honchar Dnipro National University
2024-12-01
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| Series: | Researches in Mathematics |
| Subjects: | |
| Online Access: | https://vestnmath.dnu.dp.ua/index.php/rim/article/view/435/435 |
| _version_ | 1826900444198207488 |
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| author | D. Leviatan O.V. Motorna I.O. Shevchuk |
| author_facet | D. Leviatan O.V. Motorna I.O. Shevchuk |
| author_sort | D. Leviatan |
| collection | DOAJ |
| description | In a recent paper, for a fixed $m\in\mathbb N$, we introduced trigonometric polynomials
$$
L_n(x):=\frac1{h^m}\underbrace{\int_{-h/2}^{h/2}\dots\int_{-h/2}^{h/2}}_{m\,\text{times}}J_n(x+t_1+\cdots+t_m)\,dt_1\cdots\,dt_m,
$$
where $J_n$ is a Jackson-type kernel. In the current paper we show that $L_n$ and its first $m-1$ derivatives provide approximation to the $B$-spline of degree $m-1$ and its respective derivatives. |
| first_indexed | 2025-02-17T07:08:45Z |
| format | Article |
| id | doaj.art-922e38755bdf4e088a8e9aae6af2d03c |
| institution | Directory Open Access Journal |
| issn | 2664-4991 2664-5009 |
| language | English |
| last_indexed | 2025-02-17T07:08:45Z |
| publishDate | 2024-12-01 |
| publisher | Oles Honchar Dnipro National University |
| record_format | Article |
| series | Researches in Mathematics |
| spelling | doaj.art-922e38755bdf4e088a8e9aae6af2d03c2025-01-05T19:35:29ZengOles Honchar Dnipro National UniversityResearches in Mathematics2664-49912664-50092024-12-0132210111410.15421/242422More on fast decreasing trigonometric polynomialsD. Leviatan0https://orcid.org/0000-0003-0180-5065O.V. Motorna1https://orcid.org/0009-0003-4963-3239I.O. Shevchuk2https://orcid.org/0000-0003-1140-373XTel Aviv UniversityTaras Shevchenko Kyiv National UniversityTaras Shevchenko National University of KyivIn a recent paper, for a fixed $m\in\mathbb N$, we introduced trigonometric polynomials $$ L_n(x):=\frac1{h^m}\underbrace{\int_{-h/2}^{h/2}\dots\int_{-h/2}^{h/2}}_{m\,\text{times}}J_n(x+t_1+\cdots+t_m)\,dt_1\cdots\,dt_m, $$ where $J_n$ is a Jackson-type kernel. In the current paper we show that $L_n$ and its first $m-1$ derivatives provide approximation to the $B$-spline of degree $m-1$ and its respective derivatives.https://vestnmath.dnu.dp.ua/index.php/rim/article/view/435/435b-splinesfast decreasing trigonometric polynomials |
| spellingShingle | D. Leviatan O.V. Motorna I.O. Shevchuk More on fast decreasing trigonometric polynomials Researches in Mathematics b-splines fast decreasing trigonometric polynomials |
| title | More on fast decreasing trigonometric polynomials |
| title_full | More on fast decreasing trigonometric polynomials |
| title_fullStr | More on fast decreasing trigonometric polynomials |
| title_full_unstemmed | More on fast decreasing trigonometric polynomials |
| title_short | More on fast decreasing trigonometric polynomials |
| title_sort | more on fast decreasing trigonometric polynomials |
| topic | b-splines fast decreasing trigonometric polynomials |
| url | https://vestnmath.dnu.dp.ua/index.php/rim/article/view/435/435 |
| work_keys_str_mv | AT dleviatan moreonfastdecreasingtrigonometricpolynomials AT ovmotorna moreonfastdecreasingtrigonometricpolynomials AT ioshevchuk moreonfastdecreasingtrigonometricpolynomials |