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Uniqueness properties for discrete equations and Carleman estimates

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jun 2017Embargo end date: 01 Jan 2015 Spain English Publisher:Elsevier BVJournal:Journal of Functional Analysis, volume 272, pages 4,853-4,869 (issn: 0022-1236,

Authors: Aingeru Fernández Bertolin; Luis Vega; Luis Vega;

doi: 10.1016/j.jfa.2017.03.006 , 10.48550/arxiv.1509.08545

arXiv: http://arxiv.org/abs/1509.08545

handle: 20.500.11824/655

Uniqueness properties for discrete equations and Carleman estimates

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Abstract

In the revised version, published in 2017, we improve our Carleman estimate and the method of proof of Theorem 1.1 in order to quantify the uniqueness result in the one dimensional case, proving the sharp uniqueness result conjectured by Lyubarskii, Jaming, Malinnikova and Perfekt

Using Carleman estimates, we give a lower bound for solutions to the discrete Schr��dinger equation in both dynamic and stationary settings that allows us to prove uniqueness results, under some assumptions on the decay of the solutions.

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Spain

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Keywords

Mathematics - Analysis of PDEs, Discrete Hardy uncertainty principle, FOS: Mathematics, Carleman estimates, Unique continuation, Analysis of PDEs (math.AP)

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