JAMING, Philippe; POWELL, Alexander

Métadonnées

Licence d’utilisation du document

JAMING, Philippe
Mathématiques - Analyse, Probabilités, Modélisation - Orléans [MAPMO]
Institut de Mathématiques de Bordeaux [IMB]

POWELL, Alexander
Department of Mathematics, Vanderbilt University

Langue

Article de revue

Ce document a été publié dans

Proceedings of the American Mathematical Society. 2011, vol. 139, p. 3279-3290

American Mathematical Society

Résumé en anglais

Uncertainty principles for generating systems $\{e_n\}_{n=1}^{\infty} \subset \ltwo$ are proven and quantify the interplay between $\ell^r(\N)$ coefficient stability properties and time-frequency localization with respect to $|t|^p$ power weight dispersions. As a sample result, it is proven that if the unit-norm system $\{e_n\}_{n=1}^{\infty}$ is a Schauder basis or frame for $\ltwo$ then the two dispersion sequences $\Delta(e_n)$, $\Delta(\widehat{e_n})$ and the one mean sequence $\mu(e_n)$ cannot all be bounded. On the other hand, it is constructively proven that there exists a unit-norm exact system $\{f_n\}_{n=1}^{\infty}$ in $\ltwo$ for which all four of the sequences $\Delta(f_n)$, $\Delta(\widehat{f_n})$, $\mu(f_n)$, $\mu(\widehat{f_n})$ are bounded.< Réduire

Mots clés en anglais

Compactness

exact system

frame

Schauder basis

time-frequency concentration

uncertainty principle

URI

https://oskar-bordeaux.fr/handle/20.500.12278/190171

Project ANR

Analyse Harmonique et Problèmes Inverses - ANR-07-BLAN-0247

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251