On On the approximation of functions by Jacobi – Dunkl expansion in the weighted space $\mathbb{L}_{2}^{(\alpha,\beta)}$
UDC 517.5 We prove some new estimates useful in applications  for the approximation of certain classes of functions characterized by the generalized continuity modulus from the space $\mathbb{L}_{2}^{(\alpha,\beta)}$ by partial sums of the Jacobi – Dunkl series. For t...
Збережено в:
| Дата: | 2022 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2022
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/6275 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | UDC 517.5
We prove some new estimates useful in applications  for the approximation of certain classes of functions characterized by the generalized continuity modulus from the space $\mathbb{L}_{2}^{(\alpha,\beta)}$ by partial sums of the Jacobi – Dunkl series. For this purpose, we use the generalized Jacobi – Dunkl translation operator obtained  by Vinogradov in the monograph [Theory of approximation of functions of real variable, Fizmatgiz, Moscow (1960) (in Russian)]. |
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| DOI: | 10.37863/umzh.v74i10.6275 |