A Support Theorem for the Geodesic Ray Transform of Functions
نویسنده
چکیده
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 ∈ L(M) vanishes on an appropriate open set of geodesics, then f = 0 on the set of points lying on these geodesics. Using this result, a version of Helgason’s support theorem for the geodesic ray transform is proven. The approach is based on a microlocal version of unique continuation of analytic functions.
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