dc.contributor.author | Agrawal, Divyansh | |
dc.contributor.author | Krishnan, Venkateswaran P. | |
dc.contributor.author | Sahoo, Suman Kumar | |
dc.date.accessioned | 2022-11-01T11:06:44Z | |
dc.date.available | 2022-11-01T11:06:44Z | |
dc.date.issued | 2022 | |
dc.identifier.citation | Agrawal, D., Krishnan, V. P., & Sahoo, S. K. (2022). Unique Continuation Results for Certain Generalized Ray Transforms of Symmetric Tensor Fields. <i>Journal of Geometric Analysis</i>, <i>32</i>(10), Article 245. <a href="https://doi.org/10.1007/s12220-022-00981-5" target="_blank">https://doi.org/10.1007/s12220-022-00981-5</a> | |
dc.identifier.other | CONVID_151690452 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/83748 | |
dc.description.abstract | Let Im denote the Euclidean ray transform acting on compactly supported symmetric m-tensor field distributions f, and I∗m be its formal L2 adjoint. We study a unique continuation result for the operator Nm=I∗mIm. More precisely, we show that if Nmf vanishes to infinite order at a point x0 and if the Saint-Venant operator W acting on f vanishes on an open set containing x0, then f is a potential tensor field. This generalizes two recent works of Ilmavirta and Mönkkönen who proved such unique continuation results for the ray transform of functions and vector fields/1-forms. One of the main contributions of this work is identifying the Saint-Venant operator acting on higher-order tensor fields as the right generalization of the exterior derivative operator acting on 1-forms, which makes unique continuation results for ray transforms of higher-order tensor fields possible. In the second half of the paper, we prove analogous unique continuation results for momentum ray and transverse ray transforms. | en |
dc.format.mimetype | application/pdf | |
dc.language.iso | eng | |
dc.publisher | Springer Science and Business Media LLC | |
dc.relation.ispartofseries | Journal of Geometric Analysis | |
dc.rights | In Copyright | |
dc.subject.other | UCP for ray transforms | |
dc.subject.other | symmetric tensor fields | |
dc.subject.other | tensor tomography | |
dc.subject.other | Saint-Venant operator | |
dc.title | Unique Continuation Results for Certain Generalized Ray Transforms of Symmetric Tensor Fields | |
dc.type | article | |
dc.identifier.urn | URN:NBN:fi:jyu-202211015053 | |
dc.contributor.laitos | Matematiikan ja tilastotieteen laitos | fi |
dc.contributor.laitos | Department of Mathematics and Statistics | 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.relation.issn | 1050-6926 | |
dc.relation.numberinseries | 10 | |
dc.relation.volume | 32 | |
dc.type.version | acceptedVersion | |
dc.rights.copyright | © 2022, Mathematica Josephina, Inc. | |
dc.rights.accesslevel | openAccess | fi |
dc.relation.grantnumber | 284715 HY | |
dc.relation.grantnumber | 770924 | |
dc.relation.grantnumber | 770924 | |
dc.relation.projectid | info:eu-repo/grantAgreement/EC/H2020/770924/EU//IPTheoryUnified | |
dc.subject.yso | integraaliyhtälöt | |
dc.subject.yso | inversio-ongelmat | |
dc.subject.yso | osittaisdifferentiaaliyhtälöt | |
dc.subject.yso | tomografia | |
dc.subject.yso | funktionaalianalyysi | |
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/p12392 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p17798 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p17780 | |
dc.rights.url | http://rightsstatements.org/page/InC/1.0/?language=en | |
dc.relation.doi | 10.1007/s12220-022-00981-5 | |
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 |
jyx.fundingprogram | Centre of Excellence, AoF | en |
jyx.fundingprogram | ERC Consolidator Grant | en |
jyx.fundingprogram | Huippuyksikkörahoitus, SA | fi |
jyx.fundingprogram | ERC Consolidator Grant | fi |
jyx.fundinginformation | S.K.S. was supported by Academy of Finland (Centre of Excellence in Inverse Modelling and Imaging, grant 284715) and European Research Council under Horizon 2020 (ERC CoG 770924). | |
dc.type.okm | A1 | |