Hardy uncertainty principle, convexity and parabolic evolutions

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Date
2016-09-01Author
Escauriaza L.
Kenig C.E.
Ponce G.
Vega L.
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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.