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Uniqueness for discrete Schrödinger evolutions

Jaming, P., Lyubarskii, Y., Malinnikova, E. and Perfekt, K.-M. (2018) Uniqueness for discrete Schrödinger evolutions. Revista Matemática Iberoamericana, 34 (3). pp. 949-966. ISSN 0213-2230

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To link to this item DOI: 10.4171/rmi/1011

Abstract/Summary

We prove that if a solution of the discrete time-dependent Schrödinger equation with bounded potential decays fast at two distinct times then the solution is trivial. For the free Schr¨odinger operator, as well as for operators with compactly supported time-independent potentials, a sharp analog of the Hardy uncertainty principle is obtained, using an argument based on the theory of entire functions. Logarithmic convexity of weighted norms is employed in the case of general bounded potentials.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:71567
Uncontrolled Keywords:Discrete Schrödinger equation, unique continuation, uncertainty principle
Publisher:European Mathematical Publishing House

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