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Eurasian Mathematical Journal, 2010, Volume 1, Number 3, Pages 112–133
(Mi emj31)
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This article is cited in 3 scientific papers (total in 3 papers)
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
Abstract:
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.
Keywords and phrases:
trigonometric approximation, convergence, Fourier multipliers, Jackson, Cesaro and Fejér–Korovkin kernels.
Received: 04.06.2010
Citation:
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
Linking options:
https://www.mathnet.ru/eng/emj31 https://www.mathnet.ru/eng/emj/v1/i3/p112
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Abstract page: | 332 | Full-text PDF : | 123 | References: | 54 |
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