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hal.structure.identifierMathématiques - Analyse, Probabilités, Modélisation - Orléans [MAPMO]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorJAMING, Philippe
hal.structure.identifierDepartment of Mathematics, Vanderbilt University
dc.contributor.authorPOWELL, Alexander
dc.date.accessioned2024-04-04T02:29:26Z
dc.date.available2024-04-04T02:29:26Z
dc.date.issued2011
dc.identifier.issn0002-9939
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190171
dc.description.abstractEnUncertainty 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.
dc.description.sponsorshipAnalyse Harmonique et Problèmes Inverses - ANR-07-BLAN-0247
dc.language.isoen
dc.publisherAmerican Mathematical Society
dc.subject.enCompactness
dc.subject.enexact system
dc.subject.enframe
dc.subject.enSchauder basis
dc.subject.entime-frequency concentration
dc.subject.enuncertainty principle
dc.title.enTime-frequency concentration of generating systems
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Analyse classique [math.CA]
dc.identifier.arxiv1002.4076
bordeaux.journalProceedings of the American Mathematical Society
bordeaux.page3279-3290
bordeaux.volume139
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00458658
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00458658v1
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