Pestov identities and X-ray tomography on manifolds of low regularity
| dc.contributor.author | Ilmavirta, Joonas | |
| dc.contributor.author | Kykkänen, Antti | |
| dc.date.accessioned | 2023-06-09T08:21:54Z | |
| dc.date.available | 2023-06-09T08:21:54Z | |
| dc.date.issued | 2023 | |
| dc.identifier.citation | Ilmavirta, J., & Kykkänen, A. (2023). Pestov identities and X-ray tomography on manifolds of low regularity. <i>Inverse Problems and Imaging</i>, <i>17</i>(6), 1301-1328. <a href="https://doi.org/10.3934/ipi.2023017" target="_blank">https://doi.org/10.3934/ipi.2023017</a> | |
| dc.identifier.other | CONVID_182855192 | |
| dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/87603 | |
| dc.description.abstract | We prove that the geodesic X-ray transform is injective on scalar functions and (solenoidally) on one-forms on simple Riemannian manifolds (M, g) with g ∈ C1,1. In addition to a proof, we produce a redefinition of simplicity that is compatible with rough geometry. This C1,1-regularity is optimal on the Hölder scale. The bulk of the article is devoted to setting up a calculus of differential and curvature operators on the unit sphere bundle atop this non-smooth structure. | en |
| dc.format.mimetype | application/pdf | |
| dc.language.iso | eng | |
| dc.publisher | American Institute of Mathematical Sciences (AIMS) | |
| dc.relation.ispartofseries | Inverse Problems and Imaging | |
| dc.rights | In Copyright | |
| dc.subject.other | geodesic X-ray tomography | |
| dc.subject.other | Pestov identity | |
| dc.subject.other | non-smooth geometry | |
| dc.subject.other | integral geometry | |
| dc.subject.other | inverse problems | |
| dc.title | Pestov identities and X-ray tomography on manifolds of low regularity | |
| dc.type | research article | |
| dc.identifier.urn | URN:NBN:fi:jyu-202306093672 | |
| dc.contributor.laitos | Matematiikan ja tilastotieteen laitos | fi |
| dc.contributor.laitos | Department of Mathematics and Statistics | en |
| dc.contributor.oppiaine | Matematiikka | fi |
| dc.contributor.oppiaine | Inversio-ongelmien huippuyksikkö | fi |
| dc.contributor.oppiaine | Mathematics | en |
| dc.contributor.oppiaine | Centre of Excellence in Inverse Problems | 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 | 1301-1328 | |
| dc.relation.issn | 1930-8337 | |
| dc.relation.numberinseries | 6 | |
| dc.relation.volume | 17 | |
| dc.type.version | acceptedVersion | |
| dc.rights.copyright | © 2023 American Institute of Mathematical Sciences (AIMS) | |
| dc.rights.accesslevel | openAccess | fi |
| dc.type.publication | article | |
| dc.relation.grantnumber | 351665 | |
| dc.subject.yso | tomografia | |
| dc.subject.yso | inversio-ongelmat | |
| dc.subject.yso | integraalilaskenta | |
| dc.subject.yso | differentiaaligeometria | |
| dc.subject.yso | Riemannin monistot | |
| dc.format.content | fulltext | |
| jyx.subject.uri | http://www.yso.fi/onto/yso/p17798 | |
| jyx.subject.uri | http://www.yso.fi/onto/yso/p27912 | |
| jyx.subject.uri | http://www.yso.fi/onto/yso/p7857 | |
| jyx.subject.uri | http://www.yso.fi/onto/yso/p16682 | |
| jyx.subject.uri | http://www.yso.fi/onto/yso/p39163 | |
| dc.rights.url | http://rightsstatements.org/page/InC/1.0/?language=en | |
| dc.relation.doi | 10.3934/ipi.2023017 | |
| dc.relation.funder | Research Council of Finland | en |
| dc.relation.funder | Suomen Akatemia | fi |
| jyx.fundingprogram | Academy Research Fellow, AoF | en |
| jyx.fundingprogram | Akatemiatutkija, SA | fi |
| jyx.fundinginformation | Both authors were supported by the Academy of Finland (JI by grants 332890 and 351665, AK by 336254). | |
| dc.type.okm | A1 |
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