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

DOI:
https://doi.org/10.1090/S0002-9947-06-04059-1

Published electronically:
June 20, 2006

MathSciNet review:
2231872

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Abstract: Let be a compact manifold with boundary. We consider covariant symmetric tensor fields of order two that belong to a Sobolev space . 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 .

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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:
https://doi.org/10.1090/S0002-9947-06-04059-1

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.