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Revista Matemática Iberoamericana

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Volume 34, Issue 3, 2018, pp. 949–966
DOI: 10.4171/RMI/1011

Published online: 2018-08-27

Uniqueness for discrete Schrödinger evolutions

Philippe Jaming[1], Yurii I. Lyubarskii[2], Eugenia Malinnikova[3] and Karl-Mikael Perfekt[4]

(1) Université de Bordeaux, Talence, France
(2) The Norwegian University of Science and Technology, Trondheim, Norway
(3) Norwegian University of Science and Technology, Trondheim, Norway
(4) University of Reading, UK

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.

Keywords: Discrete Schrödinger equation, unique continuation, uncertainty principle

Jaming Philippe, Lyubarskii Yurii, Malinnikova Eugenia, Perfekt Karl-Mikael: Uniqueness for discrete Schrödinger evolutions. Rev. Mat. Iberoam. 34 (2018), 949-966. doi: 10.4171/RMI/1011