Multi angle

H 1 Besov spaces in multifractal environment, and the Frisch-Parisi conjecture

Auteurs : Seuret, Stéphane (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Multifractal properties of data coming from many scientific fields (especially in turbulence) are now rigorously established. Unfortunately, the parameters measured on these data do not correspond to those mathematically obtained for the typical (or almost sure) functions in the standard functional spaces: Hölder, Sobolev, Besov…
    In this talk, we introduce very natural Besov spaces in which typical functions possess very rich scaling properties, mimicking those observed on data for instance. We obtain various characterizations of these function spaces, in terms of oscillations or wavelet coefficients.
    Combining this with the construction of almost-doubling measures with prescribed scaling properties, we are able to bring a solution to the so-called Frisch-Parisi conjecture. This is a joint work with Julien Barral (Université Paris-Nord).

    Keywords : Frisch-Parisi conjecture

    Codes MSC :
    37F35 - Conformal densities and Hausdorff dimension

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 23/01/2020
      Date de captation : 12/12/2019
      Sous collection : Research talks
      Format : MP4
      arXiv category : Functional Analysis ; Metric Geometry ; Mathematical Physics
      Domaine : Dynamical Systems & ODE
      Durée : 00:40:30
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-12-12_Seuret.mp4

    Informations sur la rencontre

    Nom de la rencontre : Jean-Morlet Chair 2019 - Conference - Thermodynamic Formalism: Dynamical Systems, Statistical Properties and their Applications / Chaire Jean-Morlet 2019 - Conférence - Formalisme thermodynamique : systèmes dynamiques, propriétés statistiques et leurs applications
    Organisateurs de la rencontre : Nicol, Matthew ; Pollicott, Mark ; Troubetzkoy, Serge ; Vaienti, Sandro
    Dates : 09/12/2019 - 13/12/2019
    Année de la rencontre : 2019
    URL Congrès : https://www.chairejeanmorlet.com/2109.html

    Citation Data

    DOI : 10.24350/CIRM.V.19586903
    Cite this video as: Seuret, Stéphane (2019). Besov spaces in multifractal environment, and the Frisch-Parisi conjecture. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19586903
    URI : http://dx.doi.org/10.24350/CIRM.V.19586903

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