Hardy Uncertainty Principle, Convexity and Parabolic Evolutions

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.

Cited by in corpus (2)

• Dynamical versions of Hardy's uncertainty principle: A survey
• On the reachable set for the one-dimensional heat equation