Kolmogorov widths of the intersection of two finite-dimensional balls

TL;DR

This paper provides order estimates for the Kolmogorov widths of the intersection of two finite-dimensional balls in various norms, advancing understanding of their geometric properties in functional analysis.

Contribution

It introduces new order estimates for Kolmogorov widths of intersections of finite-dimensional balls in different normed spaces.

Findings

Derived order estimates for Kolmogorov widths

Analyzed intersections of $p_0$- and $p_1$-balls in $l_q^m$

Extended understanding of geometric properties of these sets

Abstract

In this paper we obtain order estimates for the Kolmogorov widths of the set $B_{p_0}^m\cap \nu B_{p_1}^m$ in $l_q^m$; here $0\le n\le m/2$, $p_0>p_1$, $q<\infty$.