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H 1 Uncertainty principles for discrete Schrödinger evolutions

Auteurs : Malinnikova, Eugenia (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : We consider solutions of the semi-discrete Schrödinger equation (where time is continuous and spacial variable is discrete), $\partial_tu = i(\Delta_du + V u)$, where $\Delta_d$ is the standard discrete Laplacian on $\mathbb{Z}^n$ and $u : [0, 1] \times \mathbb{Z}^d \to \mathbb{C}$. Uncertainty principle states that a non-trivial solution of the free equation (without potential) cannot be sharply localized at two distinct times. We discuss different extensions of this result to equations with bounded potentials. The continuous case was studied in a series of articles by L. Escauriaza, C. E. Kenig, G. Ponce, and L. Vega.
    The talk is mainly based on joint work with Ph. Jaming, Yu. Lyubarskii, and K.-M. Perfekt.

    Codes MSC :
    35A02 - Uniqueness problems: global uniqueness, local uniqueness, non-uniqueness
    35Q55 - NLS-like equations (nonlinear Schrödinger)

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 13/01/16
      Date de captation : 03/12/15
      Collection : Research talks ; Analysis and its Applications ; Partial Differential Equations
      Format : MP4
      Durée : 00:45:17
      Domaine : PDE ; Analysis and its Applications
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-12-03_Malinnikova.mp4

    Informations sur la rencontre

    Nom de la rencontre : Annual conference of the functional analysis, harmonic analysis and probability Gdr research group / Journées du Gdr analyse Fonctionnelle, harmonique et probabilités
    Organisateurs de la rencontre : Abakumov, Evgeny ; Borichev, Alexander A. ; Charpentier, Stéphane ; Lyubarskii, Yurii ; Youssfi, El Hassan ; Zarouf, Rachid
    Dates : 30/11/15 - 04/12/15
    Année de la rencontre : 2015
    URL Congrès : http://conferences.cirm-math.fr/1403.html

    Citation Data

    DOI : 10.24350/CIRM.V.18906303
    Cite this video as: Malinnikova, Eugenia (2015). Uncertainty principles for discrete Schrödinger evolutions. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18906303
    URI : http://dx.doi.org/10.24350/CIRM.V.18906303


    Bibliographie

    1. Jaming, P., Lyubarskii, Y., Malinnikova, E., & Perfekt, K.M. (2015). Uniqueness for discrete Schrödinger evolutions. - http://arxiv.org/abs/1505.05398

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