We prove the logarithmic convexity of certain quantities, which measure the quadratic exponential decay at infinity and within two characteristic hyperplanes of solutions of Schr\"odinger evolutions. As a consequence we obtain some uniqueness results that generalize (a weak form of) Hardy's version of the uncertainty principle. We also obtain corresponding results for heat evolutions.
Cite this article
Carlos E. Kenig, Luis Vega, Luis Escauriaza, Gustavo Ponce, Hardy's uncertainty principle, convexity and Schrödinger evolutions. J. Eur. Math. Soc. 10 (2008), no. 4, pp. 883–907DOI 10.4171/JEMS/134