On Quality of Approximation by Families of Generalized Sampling Series.

Abstract

The quality of approximation by families of generalized sampling series in the scale of the Lp(Rd)-spaces with 0 < p ≤ +∞ is studied in terms of realizations of generalized K-functionals related to operators of multiplier type generated by homogeneous functions. The results are formulated in terms of generators of the method and of smoothness. The applications of the general scheme to methods generated by classical kernels as well as some new constructions to describe the smoothness of odd orders in terms of approximation are given. © 2009 SAMPLING PUBLISHING.