On Beurling's uncertainty principle

Xin Gao

We generalise a result of Hedenmalm to show that if a function $f$ on $\mathbb{R}$ is such that $\int_{\mathbb{R}^2} \bigl|f(x) \, \hat f(y)\bigr| \,e^{λ\left|xy\right|} \,dx\,dy =…