On the characterization of the kernel of the geodesic X-ray transform

Chappa, Eduardo

doi:10.1090/S0002-9947-06-04059-1

On the characterization of the kernel of the geodesic X-ray transform
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Trans. Amer. Math. Soc. 358 (2006), 4793-4807 Request permission

Abstract:

Let $\overline {\Omega }$ be a compact manifold with boundary. We consider covariant symmetric tensor fields of order two that belong to a Sobolev space $H^{k}(\overline {\Omega }), k \geq 1$. We prove, under the assumption that the metric is simple, that solenoidal tensor fields that belong to the kernel of the geodesic X-ray transform are smooth up to the boundary. As a corollary we obtain that they form a finite-dimensional set in $H^{k}$.

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