by Joonas Ilmavirta, Jere Lehtonen, Mikko Salo
Abstract:
We show that on a two-dimensional compact nontrapping manifold with strictly convex boundary, a piecewise constant function is determined by its integrals over geodesics. In higher dimensions, we obtain a similar result if the manifold satisfies a foliation condition. These theorems are based on iterating a local uniqueness result. Our proofs are elementary.
Reference:
Geodesic X-ray tomography for piecewise constant functions on nontrapping manifolds (Joonas Ilmavirta, Jere Lehtonen, Mikko Salo), Mathematical Proceedings of the Cambridge Philosophical Society, volume 168, number 1, pp. 29–41, 2020.
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We show that on a two-dimensional compact nontrapping manifold with strictly convex boundary, a piecewise constant function is determined by its integrals over geodesics. In higher dimensions, we obtain a similar result if the manifold satisfies a foliation condition. These theorems are based on iterating a local uniqueness result. Our proofs are elementary.
[arXiv]
Bibtex Entry:
@article{piecewise-constant-xrt,
author = {Joonas Ilmavirta and Jere Lehtonen and Mikko Salo},
title = {{Geodesic X-ray tomography for piecewise constant functions on nontrapping manifolds}},
journal = {Mathematical Proceedings of the Cambridge Philosophical Society},
volume = {168},
number = {1},
pages = {29--41},
month = jan,
year = {2020},
arxiv = {1702.07622},
doi = {10.1017/S0305004118000543},
gsid = {10578511860916863313},
url={http://users.jyu.fi/~jojapeil/pub/piecewise-constant-xrt.pdf},
abstract = {We show that on a two-dimensional compact nontrapping manifold with strictly convex boundary, a piecewise constant function is determined by its integrals over geodesics. In higher dimensions, we obtain a similar result if the manifold satisfies a foliation condition. These theorems are based on iterating a local uniqueness result. Our proofs are elementary.}
}