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Density of the span of powers of a function à la Müntz-Szasz

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorJAMING, Philippe
hal.structure.identifierInstitute of Mathematics and Informatics, University of Pécs
dc.contributor.authorSIMON, Ilona
dc.date2018
dc.date.accessioned2024-04-04T03:14:30Z
dc.date.available2024-04-04T03:14:30Z
dc.date.issued2018
dc.identifier.issn0007-4497
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194062
dc.description.abstractEnThe aim of this paper is to establish density properties in $L^p$ spaces of the span of powers of functions $\{\psi^\lambda\,:\lambda\in\Lambda\}$, $\Lambda\subset\N$ in the spirit of the M\"untz-Sz\'asz Theorem. As density is almost never achieved, we further investigate the density of powers and a modulation of powers $\{\psi^\lambda,\psi^\lambda e^{i\alpha t}\,:\lambda\in\Lambda\}$. Finally, we establish a M\"untz-Sz\'asz Theorem for density of translates of powers of cosines $\{\cos^\lambda(t-\theta_1),\cos^\lambda(t-\theta_2)\,:\lambda\in\Lambda\}$. Under some arithmetic restrictions on $\theta_1-\theta_2$, we show that density is equivalent to a M\"untz-Sz\'asz condition on $\Lambda$ and we conjecture that those arithmetic restrictions are not needed.Some links are also established with the recently introduced concept of Heisenberg Uniqueness Pairs.
dc.description.sponsorshipAnalyse Variationnelle en Tomographies photoacoustique, thermoacoustique et ultrasonore - ANR-12-BS01-0001
dc.description.sponsorshipInitiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003
dc.language.isoen
dc.publisherElsevier
dc.title.enDensity of the span of powers of a function à la Müntz-Szasz
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Analyse classique [math.CA]
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
dc.identifier.arxiv1606.09092
bordeaux.journalBulletin des Sciences Mathématiques
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01338832
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01338832v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Bulletin%20des%20Sciences%20Math%C3%A9matiques&rft.date=2018&rft.eissn=0007-4497&rft.issn=0007-4497&rft.au=JAMING,%20Philippe&SIMON,%20Ilona&rft.genre=article


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