An uncertainty principle for solutions of the Schrödinger equation on H-type groups
Résumé
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 Schrödinger equation with potential on H-type groups. This extends the free case considered by Ben Sa¨ıdSa¨ıd, Dogga and Thangavelu [BTD] and by Ludwig and Müller [LM].
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