On Beurling's uncertainty principle (Q2801728)

The author proves that if a function \(f\) and its Fourier transform \(\widehat f\) on \(\mathbb R\) are such that NEWLINE\[NEWLINE\int\int_{\mathbb R^2}|f(x)\widehat f(y)| e^{\lambda|xy|}\,dxdy=O((1-\lambda)^{-N})NEWLINE\]NEWLINE as \(\lambda\to 1^{-}\), then \(f\) is a product of a polynomial and a Gaussian. Hedenmalm's result as well as other related results follow from this. The author promises to present multivariate extensions soon.