A sharp stability estimate for tensor tomography in non-positive curvature
| dc.contributor.author | Paternain, Gabriel P. | |
| dc.contributor.author | Salo, Mikko | |
| dc.date.accessioned | 2020-11-17T06:20:20Z | |
| dc.date.available | 2020-11-17T06:20:20Z | |
| dc.date.issued | 2021 | |
| dc.identifier.citation | Paternain, G. P., & Salo, M. (2021). A sharp stability estimate for tensor tomography in non-positive curvature. <i>Mathematische Zeitschrift</i>, <i>298</i>(3-4), 1323-1344. <a href="https://doi.org/10.1007/s00209-020-02638-x" target="_blank">https://doi.org/10.1007/s00209-020-02638-x</a> | |
| dc.identifier.other | CONVID_47012953 | |
| dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/72638 | |
| dc.description.abstract | We consider the geodesic X-ray transform acting on solenoidal tensor fields on a compact simply connected manifold with strictly convex boundary and non-positive curvature. We establish a stability estimate of the form L2↦H1/2TL2↦HT1/2, where the H1/2THT1/2-space is defined using the natural parametrization of geodesics as initial boundary points and incoming directions (fan-beam geometry); only tangential derivatives at the boundary are used. The proof is based on the Pestov identity with boundary term localized in frequency. | en |
| dc.format.mimetype | application/pdf | |
| dc.language | eng | |
| dc.language.iso | eng | |
| dc.publisher | Springer | |
| dc.relation.ispartofseries | Mathematische Zeitschrift | |
| dc.rights | CC BY 4.0 | |
| dc.title | A sharp stability estimate for tensor tomography in non-positive curvature | |
| dc.type | article | |
| dc.identifier.urn | URN:NBN:fi:jyu-202011176658 | |
| 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 | 1323-1344 | |
| dc.relation.issn | 0025-5874 | |
| dc.relation.numberinseries | 3-4 | |
| dc.relation.volume | 298 | |
| dc.type.version | publishedVersion | |
| dc.rights.copyright | © The Author(s) 2020 | |
| dc.rights.accesslevel | openAccess | fi |
| dc.relation.grantnumber | 312121 | |
| dc.relation.grantnumber | 770924 | |
| dc.relation.grantnumber | 770924 | |
| dc.relation.grantnumber | 309963 | |
| dc.relation.projectid | info:eu-repo/grantAgreement/EC/H2020/770924/EU//IPTheoryUnified | |
| dc.subject.yso | inversio-ongelmat | |
| dc.subject.yso | osittaisdifferentiaaliyhtälöt | |
| dc.format.content | fulltext | |
| 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/s00209-020-02638-x | |
| 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 | Suomen Akatemia | fi |
| dc.relation.funder | Euroopan komissio | fi |
| dc.relation.funder | Suomen Akatemia | fi |
| jyx.fundingprogram | Centre of Excellence, AoF | en |
| jyx.fundingprogram | ERC Consolidator Grant | en |
| jyx.fundingprogram | Academy Project, AoF | en |
| jyx.fundingprogram | Huippuyksikkörahoitus, SA | fi |
| jyx.fundingprogram | ERC Consolidator Grant | fi |
| jyx.fundingprogram | Akatemiahanke, SA | fi |
| jyx.fundinginformation | We are very grateful to the referee for several comments that improved the presentation and in particular for suggesting a simplified proof of Lemma 4.4. GPP was supported by EPSRC Grant EP/R001898/1 and the Leverhulme trust. MS was supported by the Academy of Finland (Finnish Centre of Excellence in Inverse Modelling and Imaging, Grant Numbers 312121 and 309963) and by the European Research Council under Horizon 2020 (ERC CoG 770924). This material is based upon work supported by the National Science Foundation under Grant No. 1440140, while the authors were in residence at MSRI in Berkeley, California, during the semester on Microlocal Analysis in 2019. | |
| dc.type.okm | A1 |
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