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 sign changes by the subspaces of generalized polynomial splines with nodes at the points 2kπ /n and 2kπ /n + h, n N, k Z, h (0, 2π /n). It is shown that these subspaces are extremal for the Kolmogorov widths of the corresponding functional classes.