An uncertainty principle for solutions of the Schr{\"o}dinger equation on H-type groups

Abstract

In this paper we consider uncertainty principles for solutions of certain PDEs on H-type groups. We first prove that, contrary to the euclidean setting, the heat kernel on H-type groups is not characterized as the only solution of the heat equation that has sharp decay at 2 different times. We then prove the analogue of Hardy's Uncertainty Principle for solutions of the Schr{\"o}dinger equation with potential on H-type groups. This extends the free case considered by Ben Sa\"id, Dogga and Thangavelu [BTD] and by Ludwig and M{\"u}ller [LM].