# Time-frequency concentration of generating systems

Abstract : 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.
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Article dans une revue
Proc. A.M.S., 2011, 139, pp.3279-3290

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https://hal.archives-ouvertes.fr/hal-00458658
Contributeur : Philippe Jaming <>
Soumis le : lundi 22 février 2010 - 09:28:42
Dernière modification le : jeudi 3 mai 2018 - 15:32:06
Document(s) archivé(s) le : vendredi 18 juin 2010 - 21:35:06

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• HAL Id : hal-00458658, version 1
• ARXIV : 1002.4076

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Philippe Jaming, Alexander Powell. Time-frequency concentration of generating systems. Proc. A.M.S., 2011, 139, pp.3279-3290. 〈hal-00458658〉

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