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arXiv · 1810.10212

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

Aingeru Fernández-Bertolin·Philippe Jaming·Salvador Pérez-Esteva
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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].

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Aingeru Fernández-Bertolin, Philippe Jaming, Salvador Pérez-Esteva. 2018-10-24. An uncertainty principle for solutions of the Schr{\"o}dinger equation on H-type groups. https://arxiv.org/abs/1810.10212

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