Affiliation:
1. Osnabrueck University Institute of Mathematics Albrechtstr. 28a 49076 Osnabrück
2. Osnabrueck University Research Center of Cellular Nanoanalytics Barbarastr. 11 49076 Osnabrück
Abstract
AbstractWe consider the approximation of measures by trigonometric polynomials with respect to the p‐Wasserstein distance for general p ≥ 1. While the best approximation error decreases inversely with the polynomial degree n for every p, convolution with the Fejér kernel achieves just a 𝒪(n−1/p) rate if p > 1. Near best are approximations by convolution of the measure with higher powers of the Fejer kernel or the de la Vallée‐Poussin kernel. Finally, we consider the pointwise approximation of trigonometric polynomials interpolating the value one at the support of atomic measures.
Subject
Electrical and Electronic Engineering,Atomic and Molecular Physics, and Optics
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