The Hardy uncertainty principle revisited M. CowlingLuis EscauriazaCarlos KenigGustavo PonceLuis Vega 35B0535B60Fourier transformSchroedinger evolutions We give a real-variable proof of the Hardy uncertainty principle. The method is based on energy estimates for evolutions with positive viscosity, convexity properties of free waves with Gaussian decay at two different times, elliptic $L^2$-estimates, and the invertibility of the Fourier transform on $L^2(\mathbb{R}^n)$ and $\mathcal{S}'(\mathbb{R}^n)$. Indiana University Mathematics Journal 2010 text pdf 10.1512/iumj.2010.59.4395 10.1512/iumj.2010.59.4395 en Indiana Univ. Math. J. 59 (2010) 2007 - 2026 state-of-the-art mathematics http://iumj.org/access/