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Séminaire Analyse

Les exposés couvrent essentiellement les thématiques autour de l’analyse complexe, la théorie des opérateurs, l’analyse harmonique, l’analyse fonctionnelle, la théorie spectrale et la modélisation et le signal (responsables : Mohamed Zarrabi et Stanislas Kupin)

  • Le 2 décembre 2021 à 14:00
  • Salle de Conférences
    Rafael Tiedra (Pontifical Catholic University of Chile)
    Spectral and scattering properties of quantum walks on homogenous trees of odd degree (Séminaire Commun avec EDP - Physique Mathématiques)
    For unitary operators U_0, U in Hilbert spaces H_0, H and identification operator J:H_0→H, we present results on the derivation of a Mourre estimate for U starting from a Mourre estimate for U_0 and on the existence and completeness of the wave operators for the triple (U,U_0,J). As an application, we determine spectral and scattering properties of a class of anisotropic quantum walks on homogenous trees of odd degree with evolution operator U. In particular, we establish a Mourre estimate for U, obtain a class of locally U-smooth operators, and prove that the spectrum of U covers the whole unit circle and is purely absolutely continuous, outside possibly a finite set where U may have eigenvalues of finite multiplicity. We also show that (at least) three different choices of free evolution operators U_0 are possible for the proof of the existence and completeness of the wave operators.
  • Le 6 décembre 2021 à 13:30
  • Salle 2
    Anna Doubova (Séville)
    GT Analyse, part I, 13h30 - 14h30: Some Inverse Problems for the Burgers Equation and Related Systems
    We present the main questions and motivations related to geometric inverse problems for some PDE’s. We will focus our talk on the inverse problems concerning the one-dimensional Burgers equation and some related nonlinear systems (involving heat effects and variable density). In these problems, the goal is to find the size of the spatial interval from some appropriate boundary observations of the solution. Depending on the properties of the initial and boundary data, we prove uniqueness and non-uniqueness results. On the other hand, we also solve these inverse problems numerically and compute approximations of the interval sizes. The presented work has been performed in collaboration with Jone Apraiz, Enrique Fernández-Cara and Masahiro Yamamoto.
  • Le 6 décembre 2021 à 15:00
  • Salle 2
    Masimba Nemaire
    GT Analyse, Part II:

    TBA
  • Le 9 décembre 2021 à 14:00
  • Salle de Conférences
    Hervé Gaussier (Grenoble)
    TBA
    TBA
  • Le 6 janvier 2022 à 14:00
  • Salle de Conférences
    Séance banalisée: rencontres de l'ANR SINGFLOWS
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  • Le 13 janvier 2022 à 14:00
  • Salle de Conférences
    Nikolai Nikolski, IMB, Université de Bordeaux
    tba
    à préciser
  • Le 10 mars 2022 à 14:00
  • Salle de Conférences
    Stéphane Jaffard (Paris Est-Créteil)
    TBA
    TBA

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