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Injectivity and Stability for a Generic Class of Generalized Radon Transforms

dc.creatorHoman, Andrew
dc.creatorZhou, Hanming
dc.date.accessioned2016-06-21
dc.date.accessioned2018-11-24T23:26:49Z
dc.date.available2016-07-28T14:00:19Z
dc.date.available2018-11-24T23:26:49Z
dc.date.issued2016-06-30
dc.identifierhttps://www.repository.cam.ac.uk/handle/1810/256893
dc.identifier.urihttp://repository.aust.edu.ng/xmlui/handle/123456789/3892
dc.description.abstractLet (M, g) be an analytic, compact, Riemannian manifold with boundary, of dimension n≥2. We study a class of generalized Radon transforms, integrating over a family of hypersurfaces embedded in M, satisfying the Bolker condition (in: Quinto, Proceedings of conference “Seventy-five Years of Radon Transforms”, Hong Kong, 1994). Using analytic microlocal analysis, we prove a microlocal regularity theorem for generalized Radon transforms on analytic manifolds defined on an analytic family of hypersurfaces. We then show injectivity and stability for an open, dense subset of smooth generalized Radon transforms satisfying the Bolker condition, including the analytic ones.
dc.languageen
dc.publisherSpringer
dc.publisherJournal of Geometric Analysis
dc.rightshttp://creativecommons.org/licenses/by/4.0/
dc.rightshttp://creativecommons.org/licenses/by/4.0/
dc.rightshttp://creativecommons.org/licenses/by/4.0/
dc.rightsAttribution 4.0 International
dc.rightsAttribution 4.0 International
dc.rightsAttribution 4.0 International
dc.subjectgeneralized Radon transforms
dc.subjectBolker condition
dc.subjectMicrolocal analysis
dc.subjectanalytic microlocal analysis
dc.titleInjectivity and Stability for a Generic Class of Generalized Radon Transforms
dc.typeArticle


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