Lower bounds for widths of classes of convolutions of periodic functions in the metrics of $C$ and $L$

Abstract

We give new sufficient conditions for kernels to belong to the set $C_{y, 2n}$ introduced by Kushpel'. These conditions give the possibility of extending the set of kernels belonging to $C_{y, 2n}$. On the basis of these results, we obtain lower bounds for the Kolmogorov widths of classes of convolutions with these kernels. We show that these estimates are exact in certain important cases.