Title: Uncertainty Principle for Discrete Schrödinger Evolution
Speaker: Yurii Lyubarskii (Professor, Department of Mathematical Sciences, Norwegian University of Science and Technology)
Hosted by David Gurarie
Abstract: We prove that if a solution of a discrete time–dependent Schrödinger equation with bounded time–independent real potential decays fast at two distinct times then the solution is trivial. The continuous case was studied by L. Escauriaza, C. E. Kenig, G. Ponce, and L. Vega. We consider a semi–discrete equation, where time is continuous and spatial variables are discretized. For the free Shrödinger operator, or operators with compactly supported potential, a sharp analogue of the Hardy uncertainty principle is obtained. The argument is based on the theory of entire functions. The logarithmic convexity of weighted norms is employed for the case of general real–valued bounded potential, following the ideas developed for the continuous case. Our result for the case of a bounded potential is not optimal.
This is joint work with Ph. Jaming, Yu. Malinnikova, and K.–M. Perfekt.