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Springer, Communications in Mathematical Physics, 2(346), p. 667-678, 2015

DOI: 10.1007/s00220-015-2500-z

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Hardy Uncertainty Principle, Convexity and Parabolic Evolutions

Journal article published in 2015 by L. Escauriaza, C. E. Kenig, G. Ponce, L. Vega ORCID
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This paper is available in a repository.

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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. ; IT641-13 (GIC12/96), DMS-0968472, DMS-1265249