Open AccessOn extremal subspaces for widths of classes of convolutions
Author(s) -
N.V. Parfinovich
Publication year - 2017
Publication title -
researches in mathematics
Language(s) - English
Resource type - Journals
eISSN - 2664-5009
pISSN - 2664-4991
DOI - 10.15421/241708
Subject(s) - linear subspace , mathematics , invariant (physics) , combinatorics , polynomial , kernel (algebra) , oscillation (cell signaling) , discrete mathematics , pure mathematics , mathematical analysis , mathematical physics , biology , genetics
We obtained the exact values of the best $L_1$-approximations of the classes $K*F$ ($r\in \mathbb{N}$) of periodic functions $K*f$ such that $f$ belongs to a given rearrangement-invariant set $F$ and $K$ is $2\pi$-periodic, not increasing oscillation, kernel, by subspaces of generalized polynomial splines with nodes at points $2k\pi / n$ ($n\in \mathbb{N}$, $k\in \mathbb{Z}$). It is shown that these subspaces are extremal for the Kolmogorov widths of the corresponding functional classes.