Time-frequency concentration of generating systems
| hal.structure.identifier | Mathématiques - Analyse, Probabilités, Modélisation - Orléans [MAPMO] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | JAMING, Philippe | |
| hal.structure.identifier | Department of Mathematics, Vanderbilt University | |
| dc.contributor.author | POWELL, Alexander | |
| dc.date.accessioned | 2024-04-04T02:29:26Z | |
| dc.date.available | 2024-04-04T02:29:26Z | |
| dc.date.issued | 2011 | |
| dc.identifier.issn | 0002-9939 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190171 | |
| dc.description.abstractEn | 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. | |
| dc.description.sponsorship | Analyse Harmonique et Problèmes Inverses - ANR-07-BLAN-0247 | |
| dc.language.iso | en | |
| dc.publisher | American Mathematical Society | |
| dc.subject.en | Compactness | |
| dc.subject.en | exact system | |
| dc.subject.en | frame | |
| dc.subject.en | Schauder basis | |
| dc.subject.en | time-frequency concentration | |
| dc.subject.en | uncertainty principle | |
| dc.title.en | Time-frequency concentration of generating systems | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Analyse classique [math.CA] | |
| dc.identifier.arxiv | 1002.4076 | |
| bordeaux.journal | Proceedings of the American Mathematical Society | |
| bordeaux.page | 3279-3290 | |
| bordeaux.volume | 139 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00458658 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00458658v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Proceedings%20of%20the%20American%20Mathematical%20Society&rft.date=2011&rft.volume=139&rft.spage=3279-3290&rft.epage=3279-3290&rft.eissn=0002-9939&rft.issn=0002-9939&rft.au=JAMING,%20Philippe&POWELL,%20Alexander&rft.genre=article |
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