A strong converse inequality for generalized sampling operators

被引：0
|
作者：
Tuncer Acar
Borislav R. Draganov
机构：
[1] Selcuk University,Department of Mathematics,Faculty of Science
[2] Sofia University “St. Kliment Ohridski”,Department of Mathematics and Informatics
[3] Bulgarian Academy of Sciences,Institute of Mathematics and Informatics
来源：
Annals of Functional Analysis | 2022年 / 13卷
关键词：
Sampling operator; Sampling series; Direct inequality; Jackson-type inequality; Strong converse inequality; Converse estimate; Voronovskaja-type inequality; Bernstein-type inequality; Saturation; Modulus of smoothness; -functional; 41A17; 41A25; 41A27; 41A35; 41A40; 94A20;
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摘要：
We establish a two-term strong converse inequality for the rate of approximation of generalized sampling operators by means of the classical moduli of smoothness. It matches an already known direct estimate. We combine the direct and the converse estimates to derive the saturation property and class of this approximation operator. We demonstrate the general results for the sampling operators generated by the central B-splines, linear combinations of translates of B-splines, and the Bochner–Riesz kernel.
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