A fast converging sampling operator
Copyright policy )A fast converging sampling operator
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.
- Sofia University Bulgaria
Matematik, weighted approximation, Approximation by operators (in particular, by integral operators), weak converse estimate, Rate of convergence, degree of approximation, Weighted approximation, Mathematical Sciences, \(K\)-functional, sampling operator, Inverse theorems in approximation theory, modulus of smoothness, direct estimate, sampling series, Sampling operator;sampling series;weighted approximation;direct estimate;weak converse estimate;modulus of smoothness;$K$-functional, Inequalities in approximation (Bernstein, Jackson, Nikol'skiĭ-type inequalities), Sampling theory in information and communication theory
Matematik, weighted approximation, Approximation by operators (in particular, by integral operators), weak converse estimate, Rate of convergence, degree of approximation, Weighted approximation, Mathematical Sciences, \(K\)-functional, sampling operator, Inverse theorems in approximation theory, modulus of smoothness, direct estimate, sampling series, Sampling operator;sampling series;weighted approximation;direct estimate;weak converse estimate;modulus of smoothness;$K$-functional, Inequalities in approximation (Bernstein, Jackson, Nikol'skiĭ-type inequalities), Sampling theory in information and communication theory
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