Article

 dc.creator Hedenmalm, Håkan es dc.creator Montes Rodríguez, Alfonso es dc.date.accessioned 2016-09-23T10:59:44Z dc.date.available 2016-09-23T10:59:44Z dc.date.issued 2011 dc.identifier.citation Hedenmalm, H. y Montes Rodríguez, A. (2011). Heisenberg uniqueness pairs and the Klein-Gordon equation. Annals of Mathematics, 173, 1507-1527. dc.identifier.issn 0003-486X es dc.identifier.issn 1939-8980 es dc.identifier.uri http://hdl.handle.net/11441/45349 dc.description.abstract A 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 es 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. dc.description.sponsorship Plan Nacional I+D+I (Ministerio de Educación y Ciencia) es dc.description.sponsorship Junta de Andalucía es dc.format application/pdf es dc.language.iso eng es dc.publisher Princeton University es dc.relation.ispartof Annals of Mathematics, 173, 1507-1527. dc.rights Attribution-NonCommercial-NoDerivatives 4.0 Internacional * dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/ * dc.subject Trigonometric system es dc.subject Inversion es dc.subject Composition operator es dc.subject Klein-Gordon equation es dc.subject Ergodic theory es dc.title Heisenberg uniqueness pairs and the Klein-Gordon equation es dc.type info:eu-repo/semantics/article es dcterms.identifier https://ror.org/03yxnpp24 dc.type.version info:eu-repo/semantics/submittedVersion es dc.rights.accessRights info:eu-repo/semantics/openAccess es dc.contributor.affiliation Universidad de Sevilla. Departamento de Análisis Matemático es dc.relation.projectID MTM2006-09060 es dc.relation.projectID FQM-260 es dc.relation.projectID FQM06-02225 es dc.relation.publisherversion http://annals.math.princeton.edu/wp-content/uploads/annals-v173-n3-p06-s.pdf es dc.identifier.doi 10.4007/annals.2011.173.3.6 es dc.contributor.group Universidad de Sevilla. FQM260: Variable Compleja y Teoria de Operadores es idus.format.extent 16 p. es dc.journaltitle Annals of Mathematics es dc.publication.volumen 173 es dc.publication.initialPage 1507 es dc.publication.endPage 1527 es dc.identifier.idus https://idus.us.es/xmlui/handle/11441/45349 dc.contributor.funder Ministerio de Educación y Ciencia (MEC). España dc.contributor.funder Junta de Andalucía
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