Näytä suppeat kuvailutiedot

dc.contributor.authorPaternain, Gabriel B.
dc.contributor.authorSalo, Mikko
dc.contributor.authorUhlmann, Gunther
dc.contributor.authorZhou, Hanming
dc.date.accessioned2020-02-19T10:50:59Z
dc.date.available2020-02-19T10:50:59Z
dc.date.issued2019
dc.identifier.citationPaternain, G. B., Salo, M., Uhlmann, G., & Zhou, H. (2019). The geodesic X-ray transform with matrix weights. <i>American Journal of Mathematics</i>, <i>141</i>(6), 1707-1750. <a href="https://doi.org/10.1353/ajm.2019.0045" target="_blank">https://doi.org/10.1353/ajm.2019.0045</a>
dc.identifier.otherCONVID_34636999
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/67886
dc.description.abstractConsider a compact Riemannian manifold of dimension ≥ 3 with strictly convex boundary, such that the manifold admits a strictly convex function. We show that the attenuated ray transform in the presence of an arbitrary connection and Higgs field is injective modulo the natural obstruction for functions and one-forms. We also show that the connection and the Higgs field are uniquely determined by the scattering relation modulo gauge transformations. The proofs involve a reduction to a local result showing that the geodesic X-ray transform with a matrix weight can be inverted locally near a point of strict convexity at the boundary, and a detailed analysis of layer stripping arguments based on strictly convex exhaustion functions. As a somewhat striking corollary, we show that these integral geometry problems can be solved on strictly convex manifolds of dimension ≥ 3 having nonnegative sectional curvature (similar results were known earlier in negative sectional curvature). We also apply our methods to solve some inverse problems in quantum state tomography and polarization tomography.en
dc.format.mimetypeapplication/pdf
dc.languageeng
dc.language.isoeng
dc.publisherJohns Hopkins University Press
dc.relation.ispartofseriesAmerican Journal of Mathematics
dc.rightsIn Copyright
dc.titleThe geodesic X-ray transform with matrix weights
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202002192119
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineInversio-ongelmien huippuyksikköfi
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineCentre of Excellence in Inverse Problemsen
dc.contributor.oppiaineMathematicsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.format.pagerange1707-1750
dc.relation.issn0002-9327
dc.relation.numberinseries6
dc.relation.volume141
dc.type.versionacceptedVersion
dc.rights.copyright© 2019 by Johns Hopkins University Press
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber284715 HY
dc.relation.grantnumber307023
dc.relation.grantnumber307023
dc.relation.grantnumber309963
dc.relation.grantnumber770924
dc.relation.grantnumber770924
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/FP7/307023/EU//InvProbGeomPDE
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/H2020/770924/EU//IPTheoryUnified
dc.subject.ysointegraaliyhtälöt
dc.subject.ysoinversio-ongelmat
dc.subject.ysomonistot
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p20357
jyx.subject.urihttp://www.yso.fi/onto/yso/p27912
jyx.subject.urihttp://www.yso.fi/onto/yso/p28181
dc.rights.urlhttp://rightsstatements.org/page/InC/1.0/?language=en
dc.relation.doi10.1353/ajm.2019.0045
dc.relation.funderResearch Council of Finlanden
dc.relation.funderEuropean Commissionen
dc.relation.funderResearch Council of Finlanden
dc.relation.funderEuropean Commissionen
dc.relation.funderSuomen Akatemiafi
dc.relation.funderEuroopan komissiofi
dc.relation.funderSuomen Akatemiafi
dc.relation.funderEuroopan komissiofi
jyx.fundingprogramCentre of Excellence, AoFen
jyx.fundingprogramFP7 (EU's 7th Framework Programme)en
jyx.fundingprogramAcademy Project, AoFen
jyx.fundingprogramERC Consolidator Granten
jyx.fundingprogramHuippuyksikkörahoitus, SAfi
jyx.fundingprogramEU:n 7. puiteohjelma (FP7)fi
jyx.fundingprogramAkatemiahanke, SAfi
jyx.fundingprogramERC Consolidator Grantfi
jyx.fundinginformationResearch of the first and fourth authors supported by EPSRC grant EP/M023842/1; research of the second author supported by the Academy of Finland (Finnish Centre of Excellence in Inverse Modelling and Imaging, grant numbers 284715 and 309963) and by the European Research Council under FP7/2007-2013 (ERC StG 307023) and Horizon 2020 (ERC CoG 770924); research of the third author supported in part by the NSF.
dc.type.okmA1


Aineistoon kuuluvat tiedostot

Thumbnail

Aineisto kuuluu seuraaviin kokoelmiin

Näytä suppeat kuvailutiedot

In Copyright
Ellei muuten mainita, aineiston lisenssi on In Copyright