Exact values of the best (α, β) -approximations of classes of convolutions with kernels that do not increase the number of sign changes - Parfinovych, N. V. (Ukrains’kyi Matematychnyi Zhurnal, 2017)
We obtain the exact values of the best $(α , β )$-approximations of the classes $K * F$ of periodic functions $K * f$ such that$f$ belongs to a given rearrangement-invariant set $F$ and $K$ is $2π$ -periodic kernel that do not increase the number of signchanges by the subspaces of generalized polynomial splines with nodes at the points $2kπ /n$ and $2kπ /n + h, n \in N, k \in Z, h \in (0, 2π /n)$. It is shown that these subspaces are extremal for the Kolmogorov widths of the correspondingfunctional classes.