TY - JOUR
AU - Ilmavirta, Joonas
PY - 2015/12/14
Y2 - 2024/06/14
TI - A Reflection Approach to the Broken Ray Transform
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 117
IS - 2
SE - Articles
DO - 10.7146/math.scand.a-22869
UR - https://www.mscand.dk/article/view/22869
SP - 231-257
AB - 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 CalderÃ³n's problem with partial data, and we give implications of our results for this application.
ER -