Geodesic ray transform with matrix weights for piecewise constant functions
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2019
- DOI:
- 10.48550/arXiv.1901.03525
- arXiv:
- arXiv:1901.03525
- Bibcode:
- 2019arXiv190103525I
- Keywords:
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- Mathematics - Differential Geometry;
- 44A12;
- 65R32;
- 53A99
- E-Print:
- 10 pages, 1 figure