6533b82bfe1ef96bd128ccf9

RESEARCH PRODUCT

Geodesic ray transform with matrix weights for piecewise constant functions

Jesse RailoJoonas Ilmavirta

subject

Mathematics - Differential Geometry44A12 65R32 53A99GeodesicGeneral Mathematics010102 general mathematicsMathematical analysisConjugate pointsmatrix weight01 natural sciencesinversio-ongelmatManifoldFoliation010101 applied mathematicsMatrix (mathematics)geodesic ray transformDifferential Geometry (math.DG)Dimension (vector space)FOS: MathematicsPiecewiseConstant function0101 mathematicsintegral geometryMathematics

description

We show injectivity of the geodesic X-ray transform on piecewise constant functions when the transform is weighted by a continuous matrix weight. The manifold is assumed to be compact and nontrapping of any dimension, and in dimension three and higher we assume a foliation condition. We make no assumption regarding conjugate points or differentiability of the weight. This extends recent results for unweighted transforms.

yearjournalcountryeditionlanguage
2019-01-11
10.5186/aasfm.2020.4558http://arxiv.org/abs/1901.03525