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dc.contributor.authorRüland, Angkana
dc.contributor.authorSalo, Mikko
dc.date.accessioned2018-02-23T12:29:23Z
dc.date.available2018-02-23T12:29:23Z
dc.date.issued2018
dc.identifier.citationRüland, A., & Salo, M. (2018). Exponential instability in the fractional Calderón problem. <i>Inverse Problems</i>, <i>34</i>(4), Article 045003. <a href="https://doi.org/10.1088/1361-6420/aaac5a" target="_blank">https://doi.org/10.1088/1361-6420/aaac5a</a>
dc.identifier.otherCONVID_27888015
dc.identifier.otherTUTKAID_76734
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/57168
dc.description.abstractIn this paper we prove the exponential instability of the fractional Calderón problem and thus prove the optimality of the logarithmic stability estimate from Rüland and Salo (2017 arXiv:1708.06294). In order to infer this result, we follow the strategy introduced by Mandache in (2001 Inverse Problems 17 1435) for the standard Calderón problem. Here we exploit a close relation between the fractional Calderón problem and the classical Poisson operator. Moreover, using the construction of a suitable orthonormal basis, we also prove (almost) optimality of the Runge approximation result for the fractional Laplacian, which was derived in Rüland and Salo (2017 arXiv:1708.06294). Finally, in one dimension, we show a close relation between the fractional Calderón problem and the truncated Hilbert transform.en
dc.language.isoeng
dc.publisherInstitute of Physics
dc.relation.ispartofseriesInverse Problems
dc.subject.otherCalderón problem
dc.subject.otherPoisson operator
dc.subject.otherHilbert transform
dc.titleExponential instability in the fractional Calderón problem
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201802211557
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineMathematicsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.date.updated2018-02-21T16:15:12Z
dc.description.reviewstatuspeerReviewed
dc.relation.issn0266-5611
dc.relation.numberinseries4
dc.relation.volume34
dc.type.versionpublishedVersion
dc.rights.copyright© the Authors, 2018. This is an open access article distributed under the terms of the Creative Commons License.
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber284715 HY
dc.relation.grantnumber309963
dc.relation.grantnumber307023
dc.relation.grantnumber307023
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/FP7/307023/EU//InvProbGeomPDE
dc.subject.ysoinversio-ongelmat
jyx.subject.urihttp://www.yso.fi/onto/yso/p27912
dc.rights.urlhttps://creativecommons.org/licenses/by/3.0/
dc.relation.doi10.1088/1361-6420/aaac5a
dc.relation.funderSuomen Akatemiafi
dc.relation.funderSuomen Akatemiafi
dc.relation.funderEuroopan komissiofi
dc.relation.funderAcademy of Finlanden
dc.relation.funderAcademy of Finlanden
dc.relation.funderEuropean Commissionen
jyx.fundingprogramHuippuyksikkörahoitus, SAfi
jyx.fundingprogramAkatemiahanke, SAfi
jyx.fundingprogramEU:n 7. puiteohjelma (FP7)fi
jyx.fundingprogramCentre of Excellence, AoFen
jyx.fundingprogramAcademy Project, AoFen
jyx.fundingprogramFP7 (EU's 7th Framework Programme)en
jyx.fundinginformationMS is supported by the Academy of Finland (Finnish Centre of Excellence in Inverse Problems Research, grant numbers 284715 and 309963) and an ERC Starting Grant (grant number 307023).


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© the Authors, 2018. This is an open access article distributed under the terms of the Creative Commons License.
Except where otherwise noted, this item's license is described as © the Authors, 2018. This is an open access article distributed under the terms of the Creative Commons License.