A fast converging sampling operator

Year 2022, , 190 - 201, 01.12.2022

Borislav Draganov

https://doi.org/10.33205/cma.1172005

Cited By: 4

Abstract

We construct a sampling operator with the property that the smoother a function is, the faster its approximation is. We establish a direct estimate and a weak converse estimate of its rate of approximation in the uniform norm by means of a modulus of smoothness and a $K$-functional. The case of weighted approximation is also considered. The weights are positive and power-type with non-positive exponents at infinity. This sampling operator preserves every algebraic polynomial.

Keywords

Sampling operator, sampling series, weighted approximation, direct estimate, weak converse estimate, modulus of smoothness, $K$-functional

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