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∈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 analytic microlocal analysis.
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Communicated by Eric Todd Quinto.
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Krishnan, V.P. A Support Theorem for the Geodesic Ray Transform on Functions. J Fourier Anal Appl 15, 515–520 (2009). https://doi.org/10.1007/s00041-009-9061-5
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DOI: https://doi.org/10.1007/s00041-009-9061-5