Huang, Shanlin; Soffer, Avy Uncertainty principle, minimal escape velocities, and observability inequalities for Schrödinger equations. (English) Zbl 1472.35324 Am. J. Math. 143, No. 3, 753-781 (2021). Summary: 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 I. M. Sigal and the second author [Invent. Math. 99, No. 1, 115–143 (1990; Zbl 0702.35197)]. Such observability inequalities are closely related to unique continuation problems as well as controllability for the Schrödinger equation. Cited in 5 Documents MSC: 35Q41 Time-dependent Schrödinger equations and Dirac equations 35B40 Asymptotic behavior of solutions to PDEs 93B05 Controllability Keywords:Schrödinger equations Citations:Zbl 0702.35197 PDFBibTeX XMLCite \textit{S. Huang} and \textit{A. Soffer}, Am. J. Math. 143, No. 3, 753--781 (2021; Zbl 1472.35324) Full Text: DOI arXiv