Tensor tomography in periodic slabs

Ilmavirta, Joonas; Uhlmann, Gunther

doi:10.1016/j.jfa.2018.04.004

dc.contributor.author	Ilmavirta, Joonas
dc.contributor.author	Uhlmann, Gunther
dc.date.accessioned	2018-06-05T08:04:56Z
dc.date.available	2020-07-15T21:35:09Z
dc.date.issued	2018
dc.identifier.citation	Ilmavirta, J., & Uhlmann, G. (2018). Tensor tomography in periodic slabs. <i>Journal of Functional Analysis</i>, <i>275</i>(2), 288-299. <a href="https://doi.org/10.1016/j.jfa.2018.04.004" target="_blank">https://doi.org/10.1016/j.jfa.2018.04.004</a>
dc.identifier.other	CONVID_28024362
dc.identifier.other	TUTKAID_77488
dc.identifier.uri	https://jyx.jyu.fi/handle/123456789/58357
dc.description.abstract	The X-ray transform on the periodic slab [0, 1]×Tn, n ≥ 0, has a non-trivial kernel due to the symmetry of the manifold and presence of trapped geodesics. For tensor ﬁelds gauge freedom increases the kernel further, and the X-ray transform is not solenoidally injective unless n =0.We characterize the kernel of the geodesic X-ray transform for L2-regular m-tensors for any m ≥ 0. The characterization extends to more general manifolds, twisted slabs, including the Möbius strip as the simplest example.	fi
dc.format.mimetype	application/pdf
dc.language.iso	eng
dc.publisher	Academic Press
dc.relation.ispartofseries	Journal of Functional Analysis
dc.rights	CC BY-NC-ND 4.0
dc.subject.other	röntgentutkimus
dc.subject.other	X-ray tomography
dc.subject.other	tensor tomography
dc.subject.other	slab geometry
dc.title	Tensor tomography in periodic slabs
dc.type	article
dc.identifier.urn	URN:NBN:fi:jyu-201805252795
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	Mathematics	en
dc.type.uri	http://purl.org/eprint/type/JournalArticle
dc.date.updated	2018-05-25T12:15:12Z
dc.type.coar	http://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatus	peerReviewed
dc.format.pagerange	288-299
dc.relation.issn	0022-1236
dc.relation.numberinseries	2
dc.relation.volume	275
dc.type.version	acceptedVersion
dc.rights.copyright	© 2018 Elsevier Inc.
dc.rights.accesslevel	openAccess	fi
dc.relation.grantnumber	295853
dc.subject.yso	röntgenkuvaus
dc.subject.yso	tomografia
dc.subject.yso	inversio-ongelmat
dc.format.content	fulltext
jyx.subject.uri	http://www.yso.fi/onto/yso/p10181
jyx.subject.uri	http://www.yso.fi/onto/yso/p17798
jyx.subject.uri	http://www.yso.fi/onto/yso/p27912
dc.rights.url	https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.relation.doi	10.1016/j.jfa.2018.04.004
dc.relation.funder	Suomen Akatemia	fi
dc.relation.funder	Research Council of Finland	en
jyx.fundingprogram	Tutkijatohtori, SA	fi
jyx.fundingprogram	Postdoctoral Researcher, AoF	en
jyx.fundinginformation	J.I. was supported by the Academy of Finland (decision 295853), and he is grateful for hospitality and support offered by the University of Washington during visits. G.U. was partly supported by NSF grant DMS-1265958, a Si-Yuan Professorship at IAS, HKUST, and a FiDiPro at University of Helsinki.
dc.type.okm	A1