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A sharp stability estimate for the geodesic ray transform

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 نشر من قبل Plamen Stefanov
 تاريخ النشر 2018
  مجال البحث
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We prove a sharp $L^2to H^{1/2}$ 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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