Exact values of the best (α, β) -approximations of classes of convolutions with kernels that do not increase the number of sign changes
AbstractWe obtain the exact values of the best $(\alpha , \beta )$-approximations of the classes $K \ast F$ of periodic functions $K \ast f$ such that $f$ belongs to a given rearrangement-invariant set $F$ and $K$ is $2\pi$ -periodic kernel that do not increase the number of sign changes by the subspaces of generalized polynomial splines with nodes at the points $2k\pi /n$ and $2k\pi /n + h, n \in N, k \in Z, h \in (0, 2\pi /n)$. It is shown that these subspaces are extremal for the Kolmogorov widths of the corresponding functional classes.
How to Cite
ParfinovychN. V. “Exact Values of the Best (α, β) -Approximations of Classes of Convolutions with kernels That Do Not Increase the Number of Sign Changes”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, no. 8, Aug. 2017, pp. 1073-8, http://umj.imath.kiev.ua/index.php/umj/article/view/1759.