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The geodesic X-ray transform with a $GL(n,\mathbb{C})$-connection

dc.creatorMonard, François
dc.creatorPaternain, Gabriel Pedro
dc.date.accessioned2017-09-20
dc.date.accessioned2018-11-24T23:27:33Z
dc.date.available2017-11-10T15:58:56Z
dc.date.available2018-11-24T23:27:33Z
dc.identifierhttps://www.repository.cam.ac.uk/handle/1810/268504
dc.identifier.urihttp://repository.aust.edu.ng/xmlui/handle/123456789/4002
dc.description.abstractWe derive reconstruction formulas for a family of geodesic ray transforms with connection, defined on simple Riemannian surfaces. Such formulas provide injectivity of such all transforms in a neighbourhood of constant curvature metrics and non-unitary connections with curvature close to zero. If certain Fredholm equations are injective in the absence of connection, then for any smooth enough connection multiplied by a complex parameter, the corresponding transform is injective for all values of that parameter outside a discrete set. Range characterizations are also provided, as well as numerical illustrations.
dc.publisherSpringer
dc.subjectmath.DG
dc.subjectmath.DG
dc.subjectmath.AP
dc.titleThe geodesic X-ray transform with a $GL(n,\mathbb{C})$-connection
dc.typeArticle


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