Rational approximation of classes of convolutions of periodic functions

Abstract

In this work  the rational approximation of the classes of $2 \pi$-periodic functions which represented by the convolution of the functions from $ L_p (0, 2 \pi] $ with fixed kernels, which are given in the form of the sum of series on the system of Takenaka-Malmquist are investigated. The order estimates for values of best uniform rational approximation with fixed poles for the functions of these classes were found