A Reflection Approach to the Broken Ray Transform
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
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Mathematica ScandinavicaAuthors
Date
2015Copyright
© 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 UniversitetISSN Search the Publication Forum
0025-5521Keywords
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http://www.mscand.dk/article/view/22869Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/25384496
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