On universal sampling recovery in the uniform norm

TL;DR

This paper develops universal sampling recovery methods for anisotropic Sobolev and Nikol'skii classes of periodic functions, utilizing universal sampling discretization of the uniform norm and Fibonacci point sets for two-variable functions.

Contribution

It introduces new universal sampling recovery techniques based on discretization results and Fibonacci points, improving recovery for multivariate periodic functions.

Findings

Effective recovery methods for two-variable functions using Fibonacci points.

Universal techniques applicable to anisotropic Sobolev and Nikol'skii classes.

Enhanced bounds on sampling discretization in the uniform norm.

Abstract

It is known that results on universal sampling discretization of the square norm are useful in sparse sampling recovery with error measured in the square norm. In this paper we demonstrate how known results on universal sampling discretization of the uniform norm and recent results on universal sampling representation allow us to provide good universal methods of sampling recovery for anisotropic Sobolev and Nikol'skii classes of periodic functions of several variables. The sharpest results are obtained in the case of functions on two variables, where the Fibonacci point sets are used for recovery.