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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On the characterization of the kernel of the geodesic X-ray transform
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by Eduardo Chappa PDF
Trans. Amer. Math. Soc. 358 (2006), 4793-4807 Request permission

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
  • 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