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dc.creatorHedenmalm, Håkanes
dc.creatorMontes Rodríguez, Alfonsoes
dc.date.accessioned2016-09-23T10:59:44Z
dc.date.available2016-09-23T10:59:44Z
dc.date.issued2011
dc.identifier.citationHedenmalm, H. y Montes Rodríguez, A. (2011). Heisenberg uniqueness pairs and the Klein-Gordon equation. Annals of Mathematics, 173, 1507-1527.
dc.identifier.issn0003-486Xes
dc.identifier.issn1939-8980es
dc.identifier.urihttp://hdl.handle.net/11441/45349
dc.description.abstractA Heisenberg uniqueness pair (HUP) is a pair (Γ, Λ), where Γ is a curve in the plane and Λ is a set in the plane, with the following property: any bounded Borel measure µ in the plane supported on Γ, which is absolutely continuous with respect to arc length, and whose Fourier transform bµ vanishes on Λ, must automatically be the zero measure. We prove that when Γ is the hyperbola x1x2 = 1, and Λ is the lattice-cross Λ = (αZ × {0}) ∪ ({0} × βZ), where α, β are positive reals, then (Γ, Λ) is an HUP if and only if αβ ≤ 1; in this situation, the Fourier transform bµ of the measure solves the one-dimensional Klein-Gordon equation. Phrased differently, we show that e πiαnt , e πiβn/t , n ∈ Z, span a weak-star dense subspace in L ∞(R) if and only if αβ ≤ 1. In order to prove this theorem, some elements of linear fractional theory and ergodic theory are needed, such as the Birkhoff Ergodic Theorem. An idea parallel to the one exploited by Makarov and Poltoratski (in the context of model subspaces) is also needed. As a consequence, we solve a problem on the density of algebras generated by two inner functions raised by Matheson and Stessin.es
dc.description.sponsorshipPlan Nacional I+D+I (Ministerio de Educación y Ciencia)es
dc.description.sponsorshipJunta de Andalucíaes
dc.formatapplication/pdfes
dc.language.isoenges
dc.publisherPrinceton Universityes
dc.relation.ispartofAnnals of Mathematics, 173, 1507-1527.
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectTrigonometric systemes
dc.subjectInversiones
dc.subjectComposition operatores
dc.subjectKlein-Gordon equationes
dc.subjectErgodic theoryes
dc.titleHeisenberg uniqueness pairs and the Klein-Gordon equationes
dc.typeinfo:eu-repo/semantics/articlees
dcterms.identifierhttps://ror.org/03yxnpp24
dc.type.versioninfo:eu-repo/semantics/submittedVersiones
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses
dc.contributor.affiliationUniversidad de Sevilla. Departamento de Análisis Matemáticoes
dc.relation.projectIDMTM2006-09060es
dc.relation.projectIDFQM-260es
dc.relation.projectIDFQM06-02225es
dc.relation.publisherversionhttp://annals.math.princeton.edu/wp-content/uploads/annals-v173-n3-p06-s.pdfes
dc.identifier.doi10.4007/annals.2011.173.3.6es
dc.contributor.groupUniversidad de Sevilla. FQM260: Variable Compleja y Teoria de Operadoreses
idus.format.extent16 p.es
dc.journaltitleAnnals of Mathematicses
dc.publication.volumen173es
dc.publication.initialPage1507es
dc.publication.endPage1527es
dc.identifier.idushttps://idus.us.es/xmlui/handle/11441/45349
dc.contributor.funderMinisterio de Educación y Ciencia (MEC). España
dc.contributor.funderJunta de Andalucía

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