On the characterization of the kernel of the geodesic X-ray transform
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Abstract:
Let $\overline {\Omega }$ be a compact manifold with boundary. We consider covariant symmetric tensor fields of order two that belong to a Sobolev space $H^{k}(\overline {\Omega }), k \geq 1$. We prove, under the assumption that the metric is simple, that solenoidal tensor fields that belong to the kernel of the geodesic X-ray transform are smooth up to the boundary. As a corollary we obtain that they form a finite-dimensional set in $H^{k}$.References
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Additional Information
- Eduardo Chappa
- Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
- Address at time of publication: Department of Mathematical and Physical Sciences, Texas A&M International University, Laredo, Texas 78041-1900
- Received by editor(s): December 20, 2002
- Received by editor(s) in revised form: August 3, 2004
- Published electronically: June 20, 2006
- Additional Notes: This work was partially supported by NSF grant #DMS-00-70488 and NSF grant #DMS-9705792
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 358 (2006), 4793-4807
- MSC (2000): Primary 58Jxx; Secondary 44A12, 53Cxx
- DOI: https://doi.org/10.1090/S0002-9947-06-04059-1
- MathSciNet review: 2231872