@article{44bb37ac0dc94ff1ae3ea5ac6b4d9817,
title = "Uncertainty principle, minimal escape velocities, and observability inequalities for schr{\"O}dinger equations",
abstract = "We develop a new abstract derivation of the observability inequalities at two points in time for Schr{\"o}dinger 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 L2 (Rn). 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{\"o}dinger equation.",
author = "Shanlin Huang and Avy Soffer",
note = "Funding Information: 11801188) and the Fundamental Research Funds for the Central Universities (No. 2018KFYYXJJ041); research of the second author supported in part by the NSFC (No.11671163), NSF grant DMS-1600749. American Journal of Mathematics 143 (2021), 753–781. {\textcopyright} 2021 by Johns Hopkins University Press. Funding Information: Manuscript received June 25, 2018; revised July 22, 2019. Research of the first author supported in part by the National Natural Science Foundation of China (No. Publisher Copyright: {\textcopyright} 2021 by Johns Hopkins University Press.",
year = "2021",
doi = "10.1353/ajm.2021.0018",
language = "English (US)",
volume = "143",
pages = "753--781",
journal = "American Journal of Mathematics",
issn = "0002-9327",
publisher = "Johns Hopkins University Press",
number = "3",
}