Abstract
AbstractThe error of approximation by families of linear trigonometric polynomial operators in the scale of Lp‐spaces of periodic functions with 0 < p ⩽ +∞ is characterized with the help of realization functionals associated with operators of multiplier type describing smoothness properties of functions. The results are formulated in terms of generators of the family and of the smoothness. Applications of the general scheme to approximation methods generated by classical kernels as well as some new constructions describing smoothness of odd orders via approximation are given. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim
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