Coconvex approximation of periodic functions
Abstract
The Jackson inequality E n (f ) ≤ c ω 3 (f , π / n )
connects the value of the best uniform approximation E n (f ) of a 2π-periodic
function f : R → R by trigonometric polynomials of order ≤ n — 1 with its third modulus
of continuity ω 3 (f, t ).
In the present paper, we show that this inequality is true if continuous 2π-periodic functions that change their convexity
on [—π, π) only at every point of a fixed finite set consisting of the even number of points are approximated by polynomials coconvex to them.
English version (Springer): Ukrainian Mathematical Journal 59 (2007), no. 1, pp 28-44.
Citation Example: Zalizko V. D. Coconvex approximation of periodic functions // Ukr. Mat. Zh. - 2007. - 59, № 1. - pp. 29–43.
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