Regularity of ghosts in tensor tomography
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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.
Math Subject Classification44A12 53A45 58J40
Key Words and PhrasesIntegral geometry ray transform pseudodifferential operators
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