Observability and unique continuation inequalities for the Schrödinger equation

Abstract

In this paper, we present several observability and unique continuation inequalities for the free Schrödinger equation in the whole space. The observations in these inequalities are made either at two points in time or one point in time. These inequalities correspond to different kinds of controllability for the free Schrödinger equation. We also find that the observability inequality at two points in time is equivalent to the uncertainty principle built up in [18].

References in corpus (1)

• The sharp Hardy Uncertainty Principle for Schödinger evolutions

Cited by in corpus (4)

• Observable set, observability, interpolation inequality and spectral inequality for the heat equation in ${\mathbb{R}}^n$
• Uncertainty principle, minimal escape velocities and observability inequalities for schrödinger equations
• Time optimal sampled-data controls for heat equations
• Analyticity and observability for fractional heat equation on ${\mathbb{R}}^n$