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Eurasian Mathematical Journal, 2010, том 1, номер 3, страницы 112–133
(Mi emj31)
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Эта публикация цитируется в 3 научных статьях (всего в 3 статьях)
On convergence of families of linear polynomial operators generated by matrices of multipliers
K. Runovskia, H.-J. Schmeisserb a Sevastopol Branch of Moscow State University, Sevastopol, Ukraine
b Mathematisches Institut Friedrich-Schiller University, Jena, Germany
Аннотация:
The convergence of families of linear polynomial operators with kernels generated by matrices of multipliers is studied in the scale of the $L_p$-spaces with $0<p\le+\infty$. An element $a_{n,\,k}$ of generating matrix is represented as a sum of the value of the generator $\varphi(k/n)$ and a certain “small” remainder $r_{n,\,k}$. It is shown that under some conditions with respect to the remainder the convergence depends only on the properties of the Fourier transform of the generator $\varphi$. The results enable us to find explicit ranges for convergence of approximation methods generated by some classical kernels.
Ключевые слова и фразы:
trigonometric approximation, convergence, Fourier multipliers, Jackson, Cesaro and Fejér–Korovkin kernels.
Поступила в редакцию: 04.06.2010
Образец цитирования:
K. Runovski, H.-J. Schmeisser, “On convergence of families of linear polynomial operators generated by matrices of multipliers”, Eurasian Math. J., 1:3 (2010), 112–133
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/emj31 https://www.mathnet.ru/rus/emj/v1/i3/p112
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Страница аннотации: | 347 | PDF полного текста: | 132 | Список литературы: | 66 |
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