dc.contributor.author | Paternain, Gabriel B. | |
dc.contributor.author | Salo, Mikko | |
dc.contributor.author | Uhlmann, Gunther | |
dc.contributor.author | Zhou, Hanming | |
dc.date.accessioned | 2020-02-19T10:50:59Z | |
dc.date.available | 2020-02-19T10:50:59Z | |
dc.date.issued | 2019 | |
dc.identifier.citation | Paternain, 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.other | CONVID_34636999 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/67886 | |
dc.description.abstract | Consider 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.mimetype | application/pdf | |
dc.language | eng | |
dc.language.iso | eng | |
dc.publisher | Johns Hopkins University Press | |
dc.relation.ispartofseries | American Journal of Mathematics | |
dc.rights | In Copyright | |
dc.title | The geodesic X-ray transform with matrix weights | |
dc.type | article | |
dc.identifier.urn | URN:NBN:fi:jyu-202002192119 | |
dc.contributor.laitos | Matematiikan ja tilastotieteen laitos | fi |
dc.contributor.laitos | Department of Mathematics and Statistics | en |
dc.contributor.oppiaine | Inversio-ongelmien huippuyksikkö | fi |
dc.contributor.oppiaine | Matematiikka | fi |
dc.contributor.oppiaine | Centre of Excellence in Inverse Problems | en |
dc.contributor.oppiaine | Mathematics | en |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | |
dc.type.coar | http://purl.org/coar/resource_type/c_2df8fbb1 | |
dc.description.reviewstatus | peerReviewed | |
dc.format.pagerange | 1707-1750 | |
dc.relation.issn | 0002-9327 | |
dc.relation.numberinseries | 6 | |
dc.relation.volume | 141 | |
dc.type.version | acceptedVersion | |
dc.rights.copyright | © 2019 by Johns Hopkins University Press | |
dc.rights.accesslevel | openAccess | fi |
dc.relation.grantnumber | 284715 HY | |
dc.relation.grantnumber | 307023 | |
dc.relation.grantnumber | 307023 | |
dc.relation.grantnumber | 309963 | |
dc.relation.grantnumber | 770924 | |
dc.relation.grantnumber | 770924 | |
dc.relation.projectid | info:eu-repo/grantAgreement/EC/FP7/307023/EU//InvProbGeomPDE | |
dc.relation.projectid | info:eu-repo/grantAgreement/EC/H2020/770924/EU//IPTheoryUnified | |
dc.subject.yso | integraaliyhtälöt | |
dc.subject.yso | inversio-ongelmat | |
dc.subject.yso | monistot | |
dc.format.content | fulltext | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p20357 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p27912 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p28181 | |
dc.rights.url | http://rightsstatements.org/page/InC/1.0/?language=en | |
dc.relation.doi | 10.1353/ajm.2019.0045 | |
dc.relation.funder | Research Council of Finland | en |
dc.relation.funder | European Commission | en |
dc.relation.funder | Research Council of Finland | en |
dc.relation.funder | European Commission | en |
dc.relation.funder | Suomen Akatemia | fi |
dc.relation.funder | Euroopan komissio | fi |
dc.relation.funder | Suomen Akatemia | fi |
dc.relation.funder | Euroopan komissio | fi |
jyx.fundingprogram | Centre of Excellence, AoF | en |
jyx.fundingprogram | FP7 (EU's 7th Framework Programme) | en |
jyx.fundingprogram | Academy Project, AoF | en |
jyx.fundingprogram | ERC Consolidator Grant | en |
jyx.fundingprogram | Huippuyksikkörahoitus, SA | fi |
jyx.fundingprogram | EU:n 7. puiteohjelma (FP7) | fi |
jyx.fundingprogram | Akatemiahanke, SA | fi |
jyx.fundingprogram | ERC Consolidator Grant | fi |
jyx.fundinginformation | Research 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.okm | A1 | |