A fast converging sampling operator
Borislav R. Draganov
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.
Topics & Concepts
MathematicsOperator (biology)ConverseScalingPolynomialNorm (philosophy)Sampling (signal processing)Mathematical analysisApplied mathematicsPure mathematicsComputer scienceChemistryBiochemistryFilter (signal processing)Transcription factorComputer visionRepressorLawGeometryPolitical scienceGeneApproximation Theory and Sequence SpacesMathematical Analysis and Transform MethodsMathematical Approximation and Integration