Partial Data Problems and Unique Continuation in Scalar and Vector Field Tomography
| dc.contributor.author | Ilmavirta, Joonas | |
| dc.contributor.author | Mönkkönen, Keijo | |
| dc.date.accessioned | 2022-04-04T11:26:58Z | |
| dc.date.available | 2022-04-04T11:26:58Z | |
| dc.date.issued | 2022 | |
| dc.identifier.citation | Ilmavirta, J., & Mönkkönen, K. (2022). Partial Data Problems and Unique Continuation in Scalar and Vector Field Tomography. <i>Journal of Fourier Analysis and Applications</i>, <i>28</i>(2), Article 34. <a href="https://doi.org/10.1007/s00041-022-09907-9" target="_blank">https://doi.org/10.1007/s00041-022-09907-9</a> | |
| dc.identifier.other | CONVID_117506736 | |
| dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/80472 | |
| dc.description.abstract | We prove that if P(D) is some constant coefficient partial differential operator and f is a scalar field such that P(D)f vanishes in a given open set, then the integrals of f over all lines intersecting that open set determine the scalar field uniquely everywhere. This is done by proving a unique continuation property of fractional Laplacians which implies uniqueness for the partial data problem. We also apply our results to partial data problems of vector fields. | en |
| dc.format.mimetype | application/pdf | |
| dc.language.iso | eng | |
| dc.publisher | Birkhäuser | |
| dc.relation.ispartofseries | Journal of Fourier Analysis and Applications | |
| dc.rights | CC BY 4.0 | |
| dc.subject.other | inverse problems | |
| dc.subject.other | X-ray tomography | |
| dc.subject.other | vector field tomography | |
| dc.subject.other | region of interest tomography | |
| dc.subject.other | unique continuation | |
| dc.title | Partial Data Problems and Unique Continuation in Scalar and Vector Field Tomography | |
| dc.type | article | |
| dc.identifier.urn | URN:NBN:fi:jyu-202204042151 | |
| 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.relation.issn | 1069-5869 | |
| dc.relation.numberinseries | 2 | |
| dc.relation.volume | 28 | |
| dc.type.version | publishedVersion | |
| dc.rights.copyright | © 2022 the Authors | |
| dc.rights.accesslevel | openAccess | fi |
| dc.relation.grantnumber | 284715 HY | |
| dc.relation.grantnumber | 309963 | |
| dc.subject.yso | tomografia | |
| dc.subject.yso | inversio-ongelmat | |
| dc.subject.yso | osittaisdifferentiaaliyhtälöt | |
| 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/p12392 | |
| dc.rights.url | https://creativecommons.org/licenses/by/4.0/ | |
| dc.relation.doi | 10.1007/s00041-022-09907-9 | |
| dc.relation.funder | Research Council of Finland | en |
| dc.relation.funder | Research Council of Finland | en |
| dc.relation.funder | Suomen Akatemia | fi |
| dc.relation.funder | Suomen Akatemia | fi |
| jyx.fundingprogram | Centre of Excellence, AoF | en |
| jyx.fundingprogram | Academy Project, AoF | en |
| jyx.fundingprogram | Huippuyksikkörahoitus, SA | fi |
| jyx.fundingprogram | Akatemiahanke, SA | fi |
| jyx.fundinginformation | J.I. was supported by Academy of Finland (grants 332890 and 336254). K.M. was supported by Academy of Finland (Centre of Excellence in Inverse Modelling and Imaging, grant numbers 284715 and 309963). Open Access funding provided by University of Jyväskylä (JYU). | |
| dc.type.okm | A1 |
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