On Beurling's uncertainty principle

Abstract

We generalise a result of Hedenmalm to show that if a function $f$ on $\mathbb{R}$ is such that ${\int }_{{\mathbb{R}}^2}|f(x)\hat{f}(y)|e^{\lambda |xy|}dxdy=O((1-\lambda {)}^{-N})$ as $\lambda \to 1-$, then $f$ is the product of a polynomial and a gaussian.

References in corpus (1)

• Heisenberg's uncertainty principle in the sense of Beurling

Cited by in corpus (1)

• Dynamical versions of Hardy's uncertainty principle: A survey