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H 1 Rational approximation of functions with logarithmic singularities

Auteurs : Pushnitski, Alexander (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : I will report on the results of my recent work with Dmitri Yafaev (Rennes I). We consider functions $\omega$ on the unit circle with a finite number of logarithmic singularities. We study the approximation of $\omega$ by rational functions in the BMO norm. We find the leading term of the asymptotics of the distance in the BMO norm between $\omega$ and the set of rational functions of degree $n$ as $n$ goes to infinity. Our approach relies on the Adamyan-Arov-Krein theorem and on the study of the asymptotic behaviour of singular values of Hankel operators. In particular, we make use of the localisation principle, which allows us to combine the contributions of several singularities in one asymptotic formula.

    Codes MSC :
    41A20 - Approximation by rational functions
    47B06 - Riesz operators; eigenvalue distributions; approximation numbers, s-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
    47B35 - Toeplitz operators, Hankel operators, Wiener-Hopf operators

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 13/01/16
      Date de captation : 02/12/15
      Collection : Research talks ; Analysis and its Applications
      Format : MP4
      Durée : 00:53:08
      Domaine : Analysis and its Applications
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-12-02_Pushnitski.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.18906503
    Cite this video as: Pushnitski, Alexander (2015). Rational approximation of functions with logarithmic singularities. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18906503
    URI : http://dx.doi.org/10.24350/CIRM.V.18906503


    1. Pushnitski, A., & Yafaev, D. (2016). Best rational approximation of functions with logarithmic singularities. - http://arxiv.org/abs/1601.00882

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