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Multi angle Continuous and discrete uncertainty principles

Auteurs : Torrésani, Bruno (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Uncertainty principles go back to the early years of quantum mechanics. Originally introduced to describe the impossibility for a function to be sharply localized in both the direct and Fourier spaces, localization being measured by variance, it has been generalized to many other situations, including different representation spaces and different localization measures.
    In this talk we first review classical results on variance uncertainty inequalities (in particular Heisenberg, Robertson and Breitenberger inequalities). We then focus on discrete (and in particular finite-dimensional) situations, where variance has to be replaced with more suitable localization measures. We then present recent results on support and entropic inequalities, describing joint localization properties of vector expansions with respect to two frames.

    Keywords: uncertainty principle - variance of a function - Heisenberg inequality - support inequalities - entropic inequalities

    Codes MSC :
    26D20 - Other analytical inequalities
    42C40 - Wavelets and other special systems
    94A12 - Signal theory (characterization, reconstruction, filtering, etc.)
    94A17 - Measures of information, entropy

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 10/03/15
      Date de captation : 23/01/15
      Collection : Special events ; 30 Years of Wavelets
      Format : quicktime ; audio/x-aac
      Durée : 00:26:15
      Domaine : Analyse & Applications
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : http://videos.cirm-math.fr/2015_01_23_Torresani.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.18710403
    Cite this video as: Torrésani, Bruno (2015). Continuous and discrete uncertainty principles.CIRM .Audiovisual resource. doi:10.24350/CIRM.V.18710403
    URI : http://dx.doi.org/10.24350/CIRM.V.18710403


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