Hardy's Uncertainty Principle, Convexity and Schrödinger Evolutions

Details Hardy's Uncertainty Principle, Convexity and Schrödinger Evolutions Hardy's Uncertainty Principle, Convexity and Schrödinger Evolutions

2008-02-12

arxiv.org/abs/0802.1608v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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