by Joonas Ilmavirta, Jesse Railo
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.
Reference:
Geodesic ray transform with matrix weights for piecewise constant functions (Joonas Ilmavirta, Jesse Railo), Annales Academiae Scientiarum Fennicae Mathematica, volume 45, pp. 1095–1102, 2020.
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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.
[arXiv]
Bibtex Entry:
@article{pwc-wxrt,
author = {Joonas Ilmavirta and Jesse Railo},
title = {{Geodesic ray transform with matrix weights for piecewise constant functions}},
journal = {Annales Academiae Scientiarum Fennicae Mathematica},
volume = {45},
issue = {2},
pages = {1095--1102},
month = jul,
year = {2020},
arxiv = {1901.03525},
url = {http://users.jyu.fi/~jojapeil/pub/matrix_pwc_grt.pdf},
doi = {10.5186/aasfm.2020.4558},
gsid = {9189888261975950905},
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.}
}