Abel transforms with low regularity with applications to x-ray tomography on spherically symmetric manifolds
Hoop, M. V. D., & Ilmavirta, J. (2017). Abel transforms with low regularity with applications to x-ray tomography on spherically symmetric manifolds. Inverse Problems, 33(12), Article 124003. https://doi.org/10.1088/1361-6420/aa9423
Published in
Inverse ProblemsDate
2017Discipline
MatematiikkaInversio-ongelmien huippuyksikköMathematicsCentre of Excellence in Inverse ProblemsCopyright
© 2017 IOP Publishing Ltd
We study ray transforms on spherically symmetric
manifolds with a piecewise C
1,1 metric. Assuming the Herglotz
condition, the X-ray transform is injective on the space of L
2
functions on such manifolds. We also prove injectivity results for broken ray transforms (with and without periodicity) on such manifolds with a C
1,1 metric. To make these problems tractable in
low regularity, we introduce and study a class of generalized Abel
transforms and study their properties. This low regularity setting
is relevant for geophysical applications.
Publisher
Institute of PhysicsISSN Search the Publication Forum
0266-5611Keywords
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https://converis.jyu.fi/converis/portal/detail/Publication/27364757
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Related funder(s)
European Commission; Academy of FinlandFunding program(s)
FP7 (EU's 7th Framework Programme); Postdoctoral Researcher, AoF

The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Additional information about funding
MVdH gratefully acknowledges support from the Simons Foundation under the MATH + X program, and the National Science Foundation under grant DMS-1559587. JI was partly supported by an ERC starting grant (grant agreement no 307023) and by the Academy of Finland (decision 295853). The second author is grateful for hospitality and support offered by Rice University during visits. We would like to thank Mikko Salo and Matti Lassas for discussions. We are grateful to the anonymous referees and Tuomas Hytönen for valuable comments and suggestions.

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