Geodesic X-ray tomography for piecewise constant functions on nontrapping manifolds
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.
Main Authors
Format
Articles
Research article
Published
2020
Series
Subjects
Publication in research information system
Publisher
Cambridge University Press
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201912275493Use this for linking
Review status
Peer reviewed
ISSN
0305-0041
DOI
https://doi.org/10.1017/S0305004118000543
Language
English
Published in
Mathematical Proceedings of the Cambridge Philosophical Society
Citation
- Ilmavirta, J., Lehtonen, J., & Salo, M. (2020). Geodesic X-ray tomography for piecewise constant functions on nontrapping manifolds. Mathematical Proceedings of the Cambridge Philosophical Society, 168(1), 29-41. https://doi.org/10.1017/S0305004118000543
License
Copyright© Cambridge Philosophical Society 2018