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dc.creatorCanto Martín, Francisco Manueles
dc.creatorHedenmalm, Håkanes
dc.creatorMontes Rodríguez, Alfonsoes
dc.date.accessioned2016-09-20T11:15:39Z
dc.date.available2016-09-20T11:15:39Z
dc.date.issued2014
dc.identifier.citationCanto Martín, F.M., Hedenmalm, H. y Montes Rodríguez, A. (2014). Perron-Frobenius operators and the Klein-Gordon equation. Journal of the European Mathematical Society, 16 (1), 31-66.
dc.identifier.issn1435-9855es
dc.identifier.issn1435-9863es
dc.identifier.urihttp://hdl.handle.net/11441/45142
dc.description.abstractFor a smooth curve Γ and a set Λ in the plane R2, let AC(Γ; Λ) be the space of finite Borel measures in the plane supported on Γ, absolutely continuous with respect to the arc length and whose Fourier transform vanishes on Λ. Following [12], we say that (Γ, Λ) is a Heisenberg uniqueness pair if AC(Γ; Λ) = {0}. In the context of a hyperbola Γ, the study of Heisenberg uniqueness pairs is the same as looking for uniqueness sets Λ of a collection of solutions to the Klein-Gordon equation. In this work, we mainly address the issue of finding the dimension of AC(Γ; Λ) when it is nonzero. We will fix the curve Γ to be the hyperbola x1x2 = 1, and the set Λ = Λα,β to be the lattice-cross Λα,β = (αZ × {0}) ∪ ({0} × βZ), where α, β are positive reals. We will also consider Γ+, the branch of x1x2 = 1 where x1 > 0. In [12], it is shown that AC(Γ; Λα,β) = {0} if and only if αβ ≤ 1. Here, we show that for αβ > 1, we get a rather drastic “phase transition”: AC(Γ; Λα,β) is infinite-dimensional whenever αβ > 1. It is shown in [13] that AC(Γ+; Λα,β) = {0} if and only if αβ < 4. Moreover, at the edge αβ = 4, the behavior is more exotic: the space AC(Γ+; Λα,β) is one-dimensional. Here, we show that the dimension of AC(Γ+; Λα,β) is infinite whenever αβ > 4. Dynamical systems, and more specifically Perron-Frobenius operators, will play a prominent role in the presentation.es
dc.description.sponsorshipMinisterio de Ciencia e Innovaciónes
dc.description.sponsorshipGöran Gustafsson Foundationes
dc.description.sponsorshipJunta de Andalucíaes
dc.formatapplication/pdfes
dc.language.isoenges
dc.publisherEuropean Mathematical Societyes
dc.relation.ispartofJournal of the European Mathematical Society, 16 (1), 31-66.
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.titlePerron-Frobenius operators and the Klein-Gordon equationes
dc.typeinfo:eu-repo/semantics/articlees
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.projectIDMTM2009-09501es
dc.relation.projectIDFQM260es
dc.relation.publisherversionhttp://www.ems-ph.org/journals/show_pdf.php?issn=1435-9855&vol=16&iss=1&rank=2es
dc.identifier.doi10.4171/JEMS/427es
dc.contributor.groupUniversidad de Sevilla. FQM260: Variable Compleja y Teoria de Operadoreses
idus.format.extent27 p.es
dc.journaltitleJournal of the European Mathematical Societyes
dc.publication.volumen16es
dc.publication.issue1es
dc.publication.initialPage31es
dc.publication.endPage66es
dc.identifier.idushttps://idus.us.es/xmlui/handle/11441/45142

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