Sampling discretization in Orlicz spaces

TL;DR

This paper presents new sampling discretization results in Orlicz spaces, focusing on sampling recovery problems and analyzing errors in various Orlicz norms, especially near L^2.

Contribution

It introduces novel sampling discretization techniques in Orlicz norms and applies them to sampling recovery with a focus on linear methods close to L^2.

Findings

New bounds for sampling discretization in Orlicz spaces

Effective linear recovery methods near L^2 norms

Enhanced understanding of error behavior in Orlicz norm recovery

Abstract

We obtain new sampling discretization results in Orlicz norms on finite dimensional spaces. As applications, we study sampling recovery problems, where the error of the recovery process is calculated with respect to different Orlicz norms. In particular, we are interested in the recovery by linear methods in the norms close to $L^2$.