On the Microlocal Analysis of the Geodesic X-ray Transform with Conjugate Points
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چکیده
We study the microlocal properties of the geodesic X-ray transform X on a manifold with boundary allowing the presence of conjugate points. Assuming that there are no self-intersecting geodesics and all conjugate pairs are nonsingular we show that the normal operator N = X t ◦X can be decomposed as the sum of a pseudodifferential operator of order −1 and a sum of Fourier integral operators. We also apply this decomposition to prove inversion of X is only mildly ill-posed in dimension three or higher.
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تاریخ انتشار 2015