Widths and best approximations for classes of convolutions of periodic functions

@article{Serdyuk1999WidthsAB,
title={Widths and best approximations for classes of convolutions of periodic functions},
author={A. Serdyuk},
journal={Ukrainian Mathematical Journal},
year={1999},
volume={51},
pages={748-763}
}

We establish exact lower bounds for the Kolmogorov widths in the metrics ofC andL for classes of functions with high smoothness; the elements of these classes are sourcewise-representable as convolutions with generating kernels that can increase oscillations. We calculate the exact values of the best approximations of such classes by trigonometric polynomials.