Inversion formulas and range characterizations for the attenuated geodesic ray transform
Analysis of PDEs
2016-09-15 v1 Differential Geometry
Abstract
We present two range characterizations for the attenuated geodesic X-ray transform defined on pairs of functions and one-forms on simple surfaces. Such characterizations are based on first isolating the range over sums of functions and one-forms, then separating each sub-range in two ways, first by implicit conditions, second by deriving new inversion formulas for sums of functions and one-forms.
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Cite
@article{arxiv.1609.04361,
title = {Inversion formulas and range characterizations for the attenuated geodesic ray transform},
author = {Yernat Assylbekov and François Monard and Gunther Uhlmann},
journal= {arXiv preprint arXiv:1609.04361},
year = {2016}
}
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30 pages