Regularity of ghosts in tensor tomography |
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Authors: | Vladimir Sharafutdinov Michal Skokan Gunther Uhlmann |
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Institution: | (1) Sobolev Institute of Mathematics, 4 Koptjug Avenue, 630090 Novosibirsk, Russia;(2) Department of Mathematics, University of Washington, 98195 Seattle, WA |
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Abstract: | We study on a compact Riemannian manifold with boundary the ray transform I which integrates symmetric tensor fields over
geodesics. A tensor field is said to be a nontrivial ghost if it is in the kernel of I and is L2-orthogonal to all potential fields. We prove that a nontrivial ghost is smooth in the case of a simple metric. This implies
that the wave front set of the solenoidal part of a field f can be recovered from the ray transform If. We give an explicit
procedure for recovering the wave front set. |
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Keywords: | Math Subject Classification" target="_blank">Math Subject Classification 44A12 53A45 58J40 |
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