Uncertainty principle, minimal escape velocities and observability inequalities for schr\"{o}dinger equations

Shanlin Huang; Avy Soffer

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arXiv · 1709.09485

Uncertainty principle, minimal escape velocities and observability inequalities for schr\"{o}dinger equations

Shanlin Huang·Avy Soffer

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Abstract

We develop a new abstract derivation of the observability inequalities at two points in time for Schr\"odinger type equations. Our approach consists of two steps. In the first step we prove a Nazarov type uncertainty principle associated with a non-negative self-adjoint operator $H$ on $L^2(\mathbb{R}^n)$. In the second step we use results on asymptotic behavior of $e^{-itH}$, in particular, minimal velocity estimates introduced by Sigal and Soffer. Such observability inequalities are closely related to unique continuation problems as well as controllability for the Schr\"odinger equation.

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Shanlin Huang, Avy Soffer. 2017-09-27. Uncertainty principle, minimal escape velocities and observability inequalities for schr\"{o}dinger equations. https://arxiv.org/abs/1709.09485

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