JournalsrmiVol. 34, No. 3pp. 949–966

Uniqueness for discrete Schrödinger evolutions

  • Philippe Jaming

    Université de Bordeaux, Talence, France

  • Yurii I. Lyubarskii

    The Norwegian University of Science and Technology, Trondheim, Norway

  • Eugenia Malinnikova

    Norwegian University of Science and Technology, Trondheim, Norway

  • Karl-Mikael Perfekt

    University of Reading, UK
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Abstract

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.

Cite this article

Philippe Jaming, Yurii I. Lyubarskii, Eugenia Malinnikova, Karl-Mikael Perfekt, Uniqueness for discrete Schrödinger evolutions. Rev. Mat. Iberoam. 34 (2018), no. 3, pp. 949–966

DOI 10.4171/RMI/1011