Lp approximation with rates by multivariate generalized discrete singular operators

摘要

Here we give the approximation properties with rates of multivariate generalized discrete versions of Picard, Gauss–Weierstrass, and Poisson–Cauchy singular operators over N ≥ 1. We treat both the unitary and non-unitary cases of the operators above. We derive quantitatively Lp convergence of these operators to the unit operator by involving the Lp higher modulus of smoothness of an Lp function.