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arXiv · 1806.00707

A sharp stability estimate for the geodesic ray transform

Yernat Assylbekov·Plamen Stefanov
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Abstract

We prove a sharp $L^2\to H^{1/2}$ stability estimate for the geodesic X-ray transform of tensor fields of order $0$, $1$ and $2$ on a simple Riemannian manifold with a suitable chosen $H^{1/2}$ norm. We show that such an estimate holds for a family of such $H^{1/2}$ norms, not topologically equivalent, but equivalent on the range of the transform. The reason for this is that the geodesic X-ray transform has a microlocally structured range.

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Yernat Assylbekov, Plamen Stefanov. 2018-06-02. A sharp stability estimate for the geodesic ray transform. https://arxiv.org/abs/1806.00707

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