30 years of wavelets / 30 ans des ondelettes

Collection 30 years of wavelets / 30 ans des ondelettes

Organizer(s) Feichtinger, Hans G. ; Torrésani, Bruno

Date(s) 23/01/2015 - 24/01/2015

linked URL https://www.chairejeanmorlet.com/1523.html

00:00:00 / 00:00:00

18 18

Continuous and discrete uncertainty principles

By Bruno Torrésani

Also appears in collections : Special events, 30 Years of Wavelets, Actions thématiques

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

Information about the video

Date of recording 23/01/2015
Date of publication 10/03/2015
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.18710403
Cite this video Torrésani, Bruno (23/01/2015). Continuous and discrete uncertainty principles. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18710403
URL https://dx.doi.org/10.24350/CIRM.V.18710403

Domain(s)

Bibliography

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