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Geodesic X-ray tomography for piecewise constant functions on nontrapping manifolds

Published online by Cambridge University Press:  12 September 2018

JOONAS ILMAVIRTA ,
JERE LEHTONEN  and
MIKKO SALO
JOONAS ILMAVIRTA
Affiliation:
University of Jyväskylä, Department of Mathematics and Statistics, P.O. Box 35 (MaD), FI-40014University of Jyväskylä, Finland. e-mail: joonas.ilmavirta@jyu.fi, jere.ta.lehtonen@jyu.fi, mikko.j.salo@jyu.fi
JERE LEHTONEN
Affiliation:
University of Jyväskylä, Department of Mathematics and Statistics, P.O. Box 35 (MaD), FI-40014University of Jyväskylä, Finland. e-mail: joonas.ilmavirta@jyu.fi, jere.ta.lehtonen@jyu.fi, mikko.j.salo@jyu.fi
MIKKO SALO
Affiliation:
University of Jyväskylä, Department of Mathematics and Statistics, P.O. Box 35 (MaD), FI-40014University of Jyväskylä, Finland. e-mail: joonas.ilmavirta@jyu.fi, jere.ta.lehtonen@jyu.fi, mikko.j.salo@jyu.fi
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 168 , Issue 1 , January 2020 , pp. 29 - 41
Copyright
Copyright © Cambridge Philosophical Society 2018 

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References

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