Kolmogorov widths of an intersection of a family of balls in a mixed norm

TL;DR

This paper provides order estimates for the Kolmogorov n-widths of intersections of balls in a mixed norm space, advancing understanding of their geometric properties in high-dimensional analysis.

Contribution

It introduces new order estimates for Kolmogorov widths of intersections of balls in mixed norm spaces, extending previous results in high-dimensional geometry.

Findings

Derived order estimates for Kolmogorov n-widths

Focused on spaces with mixed norms in high dimensions

Applicable for n up to half the product of dimensions

Abstract

In this paper, order estimates for the Kolmogorov $n$-widths of an intersection of a family of balls in a mixed norm in the space $l^{m,k}_{q,\sigma}$ with $2\le q, \, \sigma <\infty$, $n\le mk/2$ are obtained.