dc.creator | Canto Martín, Francisco Manuel | es |
dc.creator | Hedenmalm, Håkan | es |
dc.creator | Montes Rodríguez, Alfonso | es |
dc.date.accessioned | 2016-09-20T11:15:39Z | |
dc.date.available | 2016-09-20T11:15:39Z | |
dc.date.issued | 2014 | |
dc.identifier.citation | Canto 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.issn | 1435-9855 | es |
dc.identifier.issn | 1435-9863 | es |
dc.identifier.uri | http://hdl.handle.net/11441/45142 | |
dc.description.abstract | For 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.sponsorship | Ministerio de Ciencia e Innovación | es |
dc.description.sponsorship | Göran Gustafsson Foundation | es |
dc.description.sponsorship | Junta de Andalucía | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | European Mathematical Society | es |
dc.relation.ispartof | Journal of the European Mathematical Society, 16 (1), 31-66. | |
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 | Perron-Frobenius operators 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 | MTM2009-09501 | es |
dc.relation.projectID | FQM260 | es |
dc.relation.publisherversion | http://www.ems-ph.org/journals/show_pdf.php?issn=1435-9855&vol=16&iss=1&rank=2 | es |
dc.identifier.doi | 10.4171/JEMS/427 | es |
dc.contributor.group | Universidad de Sevilla. FQM260: Variable Compleja y Teoria de Operadores | es |
idus.format.extent | 27 p. | es |
dc.journaltitle | Journal of the European Mathematical Society | es |
dc.publication.volumen | 16 | es |
dc.publication.issue | 1 | es |
dc.publication.initialPage | 31 | es |
dc.publication.endPage | 66 | es |
dc.identifier.idus | https://idus.us.es/xmlui/handle/11441/45142 | |