A fast converging sampling operator

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Constructive Mathematical Analysis
Volume:5 Issue:4
A fast converging sampling operator

A fast converging sampling operator

Authors : Borislav DRAGANOV

Pages : 190-201

Doi:10.33205/cma.1172005

View : 36 | Download : 5

Publication Date : 2022-12-01

Article Type : Research Paper

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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