Please use this identifier to cite or link to this item: https://hdl.handle.net/1783.1/89759
On The Microlocal Snalysis of The Geodesic X-ray Transform With Conjugate Points
| Author |
Holman, Sean
Uhlmann, Gunther Alberto Arancibia |
|---|---|
| Issue Date | 2018 |
| Source | Journal of Differential Geometry, v. 108, (3), March 2018, p. 459-494 |
| Abstract | 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 o 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 when all conjugate points are of order 1, and a certain graph condition is satisfied, in dimension three or higher. |
| ISSN |
0022-040X 1945-743X |
| Language | English |
| Type | Article |
| Access |
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