Kolmogorov widths of an intersection of anisotropic finite-dimensional balls: case $2\le q_j<\infty$

TL;DR

This paper derives order estimates for Kolmogorov n-widths of intersections of anisotropic finite-dimensional balls in specific normed spaces, extending understanding of their geometric approximation properties.

Contribution

It provides new order estimates for Kolmogorov widths of intersections of anisotropic balls in finite-dimensional spaces for the case where all q_j are at least 2.

Findings

Order estimates for Kolmogorov n-widths are established.

Results apply to intersections of anisotropic balls in finite-dimensional spaces.

The estimates extend previous knowledge to the case $2 \,\leq \, q_j < \infty$.

Abstract

Order estimates for the Kolmogorov $n$-widths of $\cap _{\alpha\in A}\nu_\alpha B^{\overline{k}}_{\overline{p}}$ in $l^{\overline{k}} _{\overline{q}}$ are obtained; here $\overline{q}=(q_1, \, \dots, \, q_d)$, $2\le q_j<\infty$, $j=1, \, \dots, \, d$.