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Approximation by families of linear trigonometric polynomial operators and smoothness properties of functions

✍ Scribed by Vladimir Rukasov; Konstantin Runovski; Hans-Jürgen Schmeisser

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
180 KB
Volume
284
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

The error of approximation by families of linear trigonometric polynomial operators in the scale of L~p~‐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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