Sampling and entropy numbers in the uniform norm

TL;DR

This paper establishes a precise relationship between sampling numbers and entropy numbers in the uniform norm for bounded convex sets of functions, providing new insights into their interplay.

Contribution

It introduces a sharp bound linking sampling and entropy numbers specifically in the context of bounded convex function sets under the uniform norm.

Findings

Established a sharp bound between sampling and entropy numbers

Enhanced understanding of function approximation in the uniform norm

Provided theoretical insights for bounded convex function sets

Abstract

We prove a sharp bound between sampling numbers and entropy numbers in the uniform norm for bounded convex sets of bounded functions.