Estimates for the error of approximation of classes of differentiable functions by Faber-Schauder partial sums

摘要

In the metric of the space phi(L) generated by a continuous even function phi(x) increasing on [0, infinity) such that phi(0) = 0, lim(x-->infinity)phi(x) = infinity one finds estimates of the error of approximation by partial sums of Faber-Schauder series in the function classes C-1 and (WH omega)-H-1, where omega(t) is a concave modulus of continuity.