Completeness of Exponentials and Beurling's Theorem on ${\mathbb{R}}^n$ and ${\mathbb{T}}^n$

Santanu Debnath, Suparna Sen

A classical result of Arne Beurling states that the Fourier transform of a nonzero complex Borel measure $\mu$ on the real line cannot vanish on a set of positive Lebesgue measure if…