Dynamic versions of Hardy’s uncertainty principle

Hardy’s uncertainty principle states that a function and its Fourier transform cannot have Gaussan decay simultaneously unless the function is identically zero if the rates of decay are too large. This result can be restated in terms of solutions to the Schrödinger equation with Gaussian decay at two different times, saying that such a solution cannot be different from the identically zero solution. In this talk, we will review this and related results, and study versions of this problem in different settings. We will discuss recent results in collaboration with A. Grecu and L. Ignat (IMAR, Bucharest) where we prove a dynamic version of Hardy’s Uncertainty principle in metric trees.