Exponential approximation and meromorphic interpolation

Abstract

We establish a relation between the approximation in $L^2[-\ddot{I}€,\ddot{I}€]$ 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 $L^2[-\ddot{I}€,\ddot{I}€]$ functions admit such an approximation.