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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the characterization of the kernel of the geodesic X-ray transform


Author: Eduardo Chappa
Journal: Trans. Amer. Math. Soc. 358 (2006), 4793-4807
MSC (2000): Primary 58Jxx; Secondary 44A12, 53Cxx
Published electronically: June 20, 2006
MathSciNet review: 2231872
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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}$.


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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

DOI: http://dx.doi.org/10.1090/S0002-9947-06-04059-1
PII: S 0002-9947(06)04059-1
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
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.