The Geodesic Ray Transform on Spherically Symmetric Reversible Finsler Manifolds

Ilmavirta, Joonas; Mönkkönen, Keijo

doi:10.1007/s12220-022-01182-w

dc.contributor.author	Ilmavirta, Joonas
dc.contributor.author	Mönkkönen, Keijo
dc.date.accessioned	2023-03-06T07:05:01Z
dc.date.available	2023-03-06T07:05:01Z
dc.date.issued	2023
dc.identifier.citation	Ilmavirta, J., & Mönkkönen, K. (2023). The Geodesic Ray Transform on Spherically Symmetric Reversible Finsler Manifolds. <i>Journal of Geometric Analysis</i>, <i>33</i>(4), Article 137. <a href="https://doi.org/10.1007/s12220-022-01182-w" target="_blank">https://doi.org/10.1007/s12220-022-01182-w</a>
dc.identifier.other	CONVID_177111625
dc.identifier.uri	https://jyx.jyu.fi/handle/123456789/85756
dc.description.abstract	We show that the geodesic ray transform is injective on scalar functions on spherically symmetric reversible Finsler manifolds where the Finsler norm satisfies a Herglotz condition. We use angular Fourier series to reduce the injectivity problem to the invertibility of generalized Abel transforms and by Taylor expansions of geodesics we show that these Abel transforms are injective. Our result has applications in linearized boundary rigidity problem on Finsler manifolds and especially in linearized elastic travel time tomography.	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	CC BY 4.0
dc.subject.other	inverse problems
dc.subject.other	geodesic ray transform
dc.subject.other	integral geometry
dc.title	The Geodesic Ray Transform on Spherically Symmetric Reversible Finsler Manifolds
dc.type	research article
dc.identifier.urn	URN:NBN:fi:jyu-202303062015
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.relation.issn	1050-6926
dc.relation.numberinseries	4
dc.relation.volume	33
dc.type.version	publishedVersion
dc.rights.copyright	© The Author(s) 2023
dc.rights.accesslevel	openAccess	fi
dc.type.publication	article
dc.relation.grantnumber	351665
dc.relation.grantnumber	351656
dc.relation.grantnumber	284715 HY
dc.relation.grantnumber	309963
dc.subject.yso	inversio-ongelmat
dc.subject.yso	differentiaaligeometria
dc.format.content	fulltext
jyx.subject.uri	http://www.yso.fi/onto/yso/p27912
jyx.subject.uri	http://www.yso.fi/onto/yso/p16682
dc.rights.url	https://creativecommons.org/licenses/by/4.0/
dc.relation.doi	10.1007/s12220-022-01182-w
dc.relation.funder	Research Council of Finland	en
dc.relation.funder	Research Council of Finland	en
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
dc.relation.funder	Suomen Akatemia	fi
dc.relation.funder	Suomen Akatemia	fi
jyx.fundingprogram	Academy Research Fellow, AoF	en
jyx.fundingprogram	Research costs of Academy Research Fellow, AoF	en
jyx.fundingprogram	Centre of Excellence, AoF	en
jyx.fundingprogram	Academy Project, AoF	en
jyx.fundingprogram	Akatemiatutkija, SA	fi
jyx.fundingprogram	Akatemiatutkijan tutkimuskulut, SA	fi
jyx.fundingprogram	Huippuyksikkörahoitus, SA	fi
jyx.fundingprogram	Akatemiahanke, SA	fi
jyx.fundinginformation	J.I. was supported by Academy of Finland (Grants 332890, 336254, 351665, 351656). K.M. was supported by Academy of Finland (Center of Excellence in Inverse Modeling and Imaging, Grant Numbers 284715 and 309963). We wish to thank the anonymous referee for feedback. Open Access funding provided by University of Jyväskylä (JYU).
dc.type.okm	A1