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dc.contributor.authorPaternain, Gabriel P.
dc.contributor.authorSalo, Mikko
dc.contributor.authorUhlmann, Gunther
dc.date.accessioned2016-11-21T12:13:44Z
dc.date.available2016-11-21T12:13:44Z
dc.date.issued2015
dc.identifier.citationPaternain, G. P., Salo, M., & Uhlmann, G. (2015). Invariant distributions, Beurling transforms and tensor tomography in higher dimensions. <em>Mathematische Annalen</em>, 363 (1-2), 305-362. <a href="https://doi.org/10.1007/s00208-015-1169-0">doi:10.1007/s00208-015-1169-0</a>
dc.identifier.otherTUTKAID_65342
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/51943
dc.description.abstractIn the recent articles [PSU13, PSU14c], a number of tensor tomography results were proved on two-dimensional manifolds. The purpose of this paper is to extend some of these methods to manifolds of any dimension. A central concept is the surjectivity of the adjoint of the geodesic ray transform, or equivalently the existence of certain distributions that are invariant under the geodesic flow. We prove that on any Anosov manifold, one can find invariant distributions with controlled first Fourier coefficients. The proof is based on subelliptic type estimates and a Pestov identity. We present an alternative construction valid on manifolds with nonpositive curvature, based on the fact that a natural Beurling transform on such manifolds turns out to be essentially a contraction. Finally, we obtain uniqueness results in tensor tomography both on simple and Anosov manifolds that improve earlier results by assuming a condition on the terminator value for a modified Jacobi equation.
dc.language.isoeng
dc.publisherSpringer Berlin Heidelberg
dc.relation.ispartofseriesMathematische Annalen
dc.subject.othertensor tomography
dc.subject.othermanifolds
dc.subject.otherinvariant distributions
dc.subject.otherBeurling transform
dc.titleInvariant distributions, Beurling transforms and tensor tomography in higher dimensions
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201611184674
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineMatematiikka
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.date.updated2016-11-18T13:15:31Z
dc.type.coarjournal article
dc.description.reviewstatuspeerReviewed
dc.format.pagerange305-362
dc.relation.issn0025-5831
dc.relation.volume363
dc.type.versionacceptedVersion
dc.rights.copyright© Springer-Verlag Berlin Heidelberg 2015. This is a final draft version of an article whose final and definitive form has been published by Springer. Published in this repository with the kind permission of the publisher.
dc.rights.accesslevelopenAccessfi
dc.relation.doi10.1007/s00208-015-1169-0


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