Hardy's Uncertainty Principle, Convexity and Schr\"odinger Evolutions
Analysis of PDEs
2008-02-13 v1
Abstract
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
@article{arxiv.0802.1608,
title = {Hardy's Uncertainty Principle, Convexity and Schr\"odinger Evolutions},
author = {L. Escauriaza and C. E. Kenig and G. Ponce and L. Vega},
journal= {arXiv preprint arXiv:0802.1608},
year = {2008}
}