Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 1095–1102

GEODESIC RAY TRANSFORM WITH MATRIX WEIGHTS FOR PIECEWISE CONSTANT FUNCTIONS

Joonas Ilmavirta and Jesse Railo

University of Jyväskylä, Department of Mathematics and Statistics
P.O. Box 35 (MaD), FI-40014 University of Jyväskylä, Finland; joonas.ilmavirta 'at' jyu.fi

University of Jyväskylä, Department of Mathematics and Statistics
P.O. Box 35 (MaD), FI-40014 University of Jyväskylä, Finland; jesse.t.railo 'at' jyu.fi

Abstract. 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.

2010 Mathematics Subject Classification: Primary 44A12, 65R32, 53A99.

Key words: Geodesic ray transform, matrix weight, integral geometry, inverse problems.

Reference to this article: J. Ilmavirta and J. Railo: Geodesic ray transform with matrix weights for piecewise constant functions. Ann. Acad. Sci. Fenn. Math. 45 (2020), 1095–1102.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4558