Uniqueness for discrete Schrödinger evolutions
Philippe JamingUniversité de Bordeaux, Talence, France
Yurii I. LyubarskiiThe Norwegian University of Science and Technology, Trondheim, Norway
Eugenia MalinnikovaNorwegian University of Science and Technology, Trondheim, Norway
Karl-Mikael PerfektUniversity 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.
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. 949–966DOI 10.4171/RMI/1011