Uncertainty principle, minimal escape velocities and observability inequalities for schrödinger equations

Abstract

We develop a new abstract derivation of the observability inequalities at two points in time for Schrödinger 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 Schrödinger equation.

revised, to appear in Amer. J. Math

References in corpus (4)

• Nazarov's uncertainty principles in higher dimension
• Abstract theory of decay estimates: perturbed Hamiltonians
• Observability and unique continuation inequalities for the Schrödinger equation
• Monotonic Local Decay Estimates

Cited by in corpus (2)

• Observable set, observability, interpolation inequality and spectral inequality for the heat equation in ${\mathbb{R}}^n$
• Stability of propagation features under time-asymptotic approximations for a class of dispersive equations