Can I read Uncertainty Principle, Minimal Escape Velocities and Observability Inequalities for Schr\"{o}dinger Equations on EtoBox?

Uncertainty Principle, Minimal Escape Velocities and Observability Inequalities for Schr\"{o}dinger Equations by Huang, Shanlin; Soffer, Avy is a scholarly article available to read on EtoBox.

What is Uncertainty Principle, Minimal Escape Velocities and Observability Inequalities for Schr\"{o}dinger Equations about?

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.

Author

Huang, Shanlin; Soffer, Avy

Published

2017

Language

EN