Premium
Approximation by families of linear trigonometric polynomial operators and smoothness properties of functions
Author(s) -
Rukasov Vladimir,
Runovski Konstantin,
Schmeisser HansJürgen
Publication year - 2011
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200810180
Subject(s) - mathematics , smoothness , trigonometry , trigonometric functions , trigonometric polynomial , multiplier (economics) , polynomial , linear operators , realization (probability) , pure mathematics , mathematical analysis , discrete mathematics , statistics , geometry , bounded function , economics , macroeconomics
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