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
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.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 | |