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arXiv · 1506.05670

Hardy Uncertainty Principle, Convexity and Parabolic Evolutions

L. Escauriaza·C. E. Kenig·G. Ponce·L. Vega
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Abstract

We give a new proof of the $L^2$ version of Hardy's uncertainty principle based on calculus and on its dynamical version for the heat equation. The reasonings rely on new log-convexity properties and the derivation of optimal Gaussian decay bounds for solutions to the heat equation with Gaussian decay at a future time. We extend the result to heat equations with lower order variable coefficient.

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L. Escauriaza, C. E. Kenig, G. Ponce, L. Vega. 2015-06-18. Hardy Uncertainty Principle, Convexity and Parabolic Evolutions. https://doi.org/10.1007/s00220-015-2500-z

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