Exponential approximation and meromorphic interpolation

TL;DR

This paper explores the connection between exponential approximation in L^2 spaces and meromorphic interpolation at integers, revealing that typical functions can be approximated using frequencies of low Beurling--Malliavin density.

Contribution

It establishes a novel relation between exponential approximation and meromorphic interpolation, extending understanding of function approximation in harmonic analysis.

Findings

Typical L^2 functions admit exponential approximation with certain frequency sets.

A relation between approximation density and meromorphic interpolation is established.

The work advances theoretical understanding of function approximation in harmonic analysis.

Abstract

We establish a relation between the approximation in $L^2[-\pi,\pi]$ by exponentials with the set of frequencies of Beurling--Malliavin density less than $1$ and the meromorphic interpolation at $\mathbb Z$. Furthermore, we show that typical $L^2[-\pi,\pi]$ functions admit such an approximation.