Uniqueness of solutions to Schrödinger equations on H-type groups

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1 Analyse IECL - Institut Élie Cartan de Lorraine 2 Indian institut of science Bangalore

Abstract : This paper deals with the Schrodinger 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 $| f{\bf z},t| \lesssim q \alpha{\bf z},t,$ where $q s$ is the heat kernel associated to $\cal L.$ If in addition $|u{\bf z},t;s 0|\lesssim q \beta{\bf z},t,$ for some $s 0\in \mathbb R\setminus\{0\},$ then we prove that $u{\bf z},t;s=0$ for all $s\in \mathbb R$ whenever \$\alpha\beta

Author: Salem Ben Saïd - Sundaram Thangavelu - Naidu Dogga -

Source: https://hal.archives-ouvertes.fr/