2017
Том 69
№ 9

Kolmogorov and linear widths of classes of s-monotone integrable functions

Konovalov V. N.

Abstract

Let $s \in \mathbb{N}$ and let $\Delta^s_+$ be the set of functions $x \mapsto \mathbb{R}$ on a finite interval $I$ such that the divided differences $[x; t_0, ... , t_s ]$ of order $s$ of these functions are nonnegative for all collections of $s + 1$ distinct points $t_0,..., t_s \in I$. For the classes $\Delta^s_+ B_p := \Delta^s_+ \bigcap B_p$ , where $B_p$ is the unit ball in $L_p$, we obtain orders of the Kolmogorov and linear widths in the spaces $L_q$ for $1 \leq q < p \leq \infty$.

English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 12, pp 1911-1936.

Citation Example: Konovalov V. N. Kolmogorov and linear widths of classes of s-monotone integrable functions // Ukr. Mat. Zh. - 2005. - 57, № 12. - pp. 1633–1652.

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