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A Reflection Approach to the Broken Ray Transform

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Ilmavirta, J. (2015). A Reflection Approach to the Broken Ray Transform. Mathematica Scandinavica, 117(2), 231-257. https://doi.org/10.7146/math.scand.a-22869
Published in
Mathematica Scandinavica
Authors
Ilmavirta, Joonas
Date
2015
Discipline
MatematiikkaMathematics
Copyright
© Aarhus Universitet, 2015. Published in this repository with the kind permission of the publisher.

 
We reduce the broken ray transform on some Riemannian manifolds (with corners) to the geodesic ray transform on another manifold, which is obtained from the original one by reflection. We give examples of this idea and present injectivity results for the broken ray transform using corresponding earlier results for the geodesic ray transform. Examples of manifolds where the broken ray transform is injective include Euclidean cones and parts of the spheres S n. In addition, we introduce the periodic broken ray transform and use the reflection argument to produce examples of manifolds where it is injective. We also give counterexamples to both periodic and nonperiodic cases. The broken ray transform arises in Calder´on’s problem with partial data, and we give implications of our results for this application.
Publisher
Aarhus Universitet
ISSN Search the Publication Forum
0025-5521
Keywords
broken ray transform matematiikka

Original source
http://www.mscand.dk/article/view/22869

DOI
https://doi.org/10.7146/math.scand.a-22869
URI

http://urn.fi/URN:NBN:fi:jyu-201512224124

Publication in research information system

https://converis.jyu.fi/converis/portal/detail/Publication/25384496

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