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arXiv · 0711.3936

A Support Theorem for the Geodesic Ray Transform of Functions

V. Krishnan
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Abstract

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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V. Krishnan. 2008-03-29. A Support Theorem for the Geodesic Ray Transform of Functions. https://arxiv.org/abs/0711.3936

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