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hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorJAMING, Philippe
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorKELLAY, Karim
dc.date.accessioned2024-04-04T03:22:09Z
dc.date.available2024-04-04T03:22:09Z
dc.date.issued2018
dc.identifier.issn0021-7670
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194728
dc.description.abstractEnLet $\Lambda$ be a set of lines in $\mathbb{R}^2$ that intersect at the origin. For $\Gamma\subset\mathbb{R}^2$ a smooth curve, we denote by $\mathcal{A}\mathcal{C}(\Gamma)$ the subset of finite measures on $\Gamma$ that are absolutely continuous with respect to arc length on $\Gamma$. For such a $\mu$, $\widehat{\mu}$ denotes the Fourier transform of $\mu$. Following Hendenmalm and Montes-Rodríguez, we will say that $(\Gamma,\Lambda)$ is a Heisenberg Uniqueness Pair if $\mu\in\mathcal{A}\mathcal{C}(\Gamma)$ is such that $\widehat{\mu}=0$ on $\Lambda$, then $\mu=0$. The aim of this paper is to provide new tools to establish this property. To do so, we will reformulate the fact that $\widehat{\mu}$ vanishes on $\Lambda$ in terms of an invariance property of $\mu$ induced by $\Lambda$. This leads us to a dynamical system on $\Gamma$ generated by $\Lambda$. The investigation of this dynamical system allows us to establish that $(\Gamma,\Lambda)$ is a Heisenberg Uniqueness Pair. This way we both unify proofs of known cases (circle, parabola, hyperbola) and obtain many new examples. This method also allows to have a better geometric intuition on why $(\Gamma,\Lambda)$ is a Heisenberg Uniqueness Pair.
dc.description.sponsorshipConséquences à long terme de l'exposition péripubertaire aux cannabinoides: étude comportementale et transcriptionnelle chez le rat et analyse moléculaire chez l'homme - ANR-06-NEUR-0044
dc.language.isoen
dc.publisherSpringer
dc.subject.enUncertainty principles
dc.subject.enannihilating pairs
dc.subject.enHeisenberg pairs
dc.title.enA dynamical system approach to Heisenberg Uniqueness Pairs
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Analyse classique [math.CA]
dc.identifier.arxiv1312.6236
bordeaux.journalJournal d'analyse mathématique
bordeaux.page273-301
bordeaux.volume134
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00921685
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00921685v1
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