Time-frequency concentration of generating systems
JAMING, Philippe
Mathématiques - Analyse, Probabilités, Modélisation - Orléans [MAPMO]
Institut de Mathématiques de Bordeaux [IMB]
Mathématiques - Analyse, Probabilités, Modélisation - Orléans [MAPMO]
Institut de Mathématiques de Bordeaux [IMB]
JAMING, Philippe
Mathématiques - Analyse, Probabilités, Modélisation - Orléans [MAPMO]
Institut de Mathématiques de Bordeaux [IMB]
< Reduce
Mathématiques - Analyse, Probabilités, Modélisation - Orléans [MAPMO]
Institut de Mathématiques de Bordeaux [IMB]
Language
en
Article de revue
This item was published in
Proceedings of the American Mathematical Society. 2011, vol. 139, p. 3279-3290
American Mathematical Society
English 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 ...Read more >
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.Read less <
English Keywords
Compactness
exact system
frame
Schauder basis
time-frequency concentration
uncertainty principle
ANR Project
Analyse Harmonique et Problèmes Inverses - ANR-07-BLAN-0247
Origin
Hal imported