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arXiv · 1006.5310

Uniqueness of solutions to the Schrodinger equation on the Heisenberg group

Salem Ben Said·Sundaram Thangavelu
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Abstract

This paper deals with the Schr{\"o}dinger equation $i\partial_s u({\bf z},t;s)-\cal L u({\bf z}, t;s)=0,$ where $\cal L$ is the sub-Laplacian on the Heisenberg group. Assume that the initial data $f$ satisfies $| f({\bf z},t)| \leq C q_a({\bf z},t),$ where $q_s$ is the heat kernel associated to $\cal L.$ If in addition $ |u({\bf z},t;s_0)|\leq C q_b({\bf z},t),$ for some $s_0\in \R^*,$ then we prove that $u({\bf z},t;s)=0$ for all $s\in \R $ whenever $ab<s_0^2.$ This result also holds true on $H$-type groups.

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Salem Ben Said, Sundaram Thangavelu. 2010-06-28. Uniqueness of solutions to the Schrodinger equation on the Heisenberg group. https://arxiv.org/abs/1006.5310

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