CIRM - Videos & books Library - Continuous and discrete uncertainty principles

Multi angle

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

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Hennenfent, Guillaume

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https://videos.cirm-math.fr/2015_01_23_Torresani.mp4

Informations sur la Rencontre

Nom de la rencontre : 30 years of wavelets / 30 ans des ondelettes
Organisateurs de la rencontre : Feichtinger, Hans G. ; Torrésani, Bruno
Dates : 23/01/15 - 24/01/15
Année de la rencontre : 2015
URL Congrès : https://www.chairejeanmorlet.com/1523.html

Données de citation

DOI : 10.24350/CIRM.V.18710403
Citer cette vidéo: 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

Bibliographie

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