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Multi angle Wavelet: from statistic to geometry

Auteurs : Kerkyacharian, Gérard (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Since the last twenty years, Littlewood-Paley analysis and wavelet theory has proved to be a very useful tool for non parametric statistic. This is essentially due to the fact that the regularity spaces (Sobolev and Besov) could be characterized by wavelet coefficients. Then it appeared that that the Euclidian analysis is not always appropriate, and lot of statistical problems have their own geometry. For instance: Wicksell problem and Jacobi Polynomials, Tomography and the harmonic analysis of the ball, the study of the Cosmological Microwave Background and the harmonic analysis of the sphere. In these last years it has been proposed to build a Littlewood-Paley analysis and a wavelet theory associated to the Laplacien of a Riemannian manifold or more generally a positive operator associated to a suitable Dirichlet space with a good behavior of the associated heat kernel. This can help to revisit some classical studies of the regularity of Gaussian field.

    Keywords: heat kernel - functional calculus - wavelet - Gaussian process

    Codes MSC :
    43A85 - Analysis on homogeneous spaces
    58C50 - Analysis on supermanifolds or graded manifolds
    60G15 - Gaussian processes
    60G17 - Sample path properties

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 16/03/15
      Date de captation : 24/01/15
      Collection : Special events ; 30 Years of Wavelets
      Format : quicktime ; audio/x-aac
      Durée : 00:25:25
      Domaine : Analyse & Applications ; Probability & Statistics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : http://videos.cirm-math.fr/2015-01-24_Kerkyacharian.mp4

    Informations sur la rencontre

    Nom du congrès : 30 years of wavelets / 30 ans des ondelettes
    Organisteurs Congrès : Feichtinger, Hans G. ; Torrésani, Bruno
    Dates : 23/01/15 - 24/01/15
    Année de la rencontre : 2015
    URL Congrès : http://feichtingertorresani.weebly.com/3...

    Citation Data

    DOI : 10.24350/CIRM.V.18724103
    Cite this video as: Kerkyacharian, Gérard (2015). Wavelet: from statistic to geometry.CIRM .Audiovisual resource. doi:10.24350/CIRM.V.18724103
    URI : http://dx.doi.org/10.24350/CIRM.V.18724103


    Voir aussi

    Bibliographie

    1. [1] Coulhon, T., Kerkyacharian, G., & Petrushev, P. (2012). Heat kernel generated frames in the setting of Dirichlet spaces. Journal of Fourier Analysis and Applications, 18(5), 995-1066 - http://dx.doi.org/10.1007/s00041-012-9232-7

    2. [2] Kerkyacharian, G., & Petrushev, P. (2015). Heat kernel based decomposition of spaces of distributions in the framework of Dirichlet space. Transactions of the American Mathematical Society, 367(1), 121-189 - http://dx.doi.org/10.1090/S0002-9947-2014-05993-X

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