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

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, 2017. (To appear.)
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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}, note = {To appear.}, month = feb, year = {2017}, arxiv = {1702.07622}, 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.} }

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