Uniqueness results for discrete Shrödinger evolution

Philippe Jaming (1) , Yurii Lyubarskii (2) , Eugenia Malinnikova (2) , Karl-Mikael Perfekt (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 Department of Mathematical Sciences

We prove that if a solution of the discrete time-dependent Schrödinger equation with bounded time-independent real potential decays fast at two distinct times then the solution is trivial. For the free Shrödinger operator or operators with compactly supported potential a sharp analog of the Hardy uncertainty principle is obtained. The argument is based on the theory of entire functions. Logarithmic convexity of weighted norms is employed for the case of general real-valued bounded potential, for this case the result is not optimal.

Domaines: Analyse classique [math.CA]; Analyse fonctionnelle [math.FA]; Variables complexes [math.CV]

Philippe Jaming, Yurii Lyubarskii, Eugenia Malinnikova, Karl-Mikael Perfekt. Uniqueness results for discrete Shrödinger evolution. Revista Matemática Iberoamericana, 2018, 34, pp.949-966. ⟨hal-01163977⟩