A Support Theorem for the Geodesic Ray Transform of Functions

Details A Support Theorem for the Geodesic Ray Transform of Functions A Support Theorem for the Geodesic Ray Transform of Functions

2007-11-26

arxiv.org/abs/0711.3936v2

Mathematics

Differential Geometry

6 pages, errors corrected, paper revised

Scientific paper

Let $(M,g)$ be a simple Riemannian manifold. Under the assumption that the
metric $g$ is real-analytic, it is shown that if the geodesic ray transform of
a function $f\in L^{2}(M)$ vanishes on an appropriate open set of geodesics,
then $f=0$ on the set of points lying on these geodesics. The approach is based
on a microlocal version of unique continuation of analytic functions.

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