A generalization of the Mader-Helgason inversion formulas for Radon transforms
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- by Y. A. Antipov and B. Rubin PDF
- Trans. Amer. Math. Soc. 364 (2012), 6479-6493 Request permission
Abstract:
In 1927, Philomena Mader derived elegant inversion formulas for the hyperplane Radon transform on $\mathbb {R}^n$. These formulas differ from the original ones by Radon and seem to be forgotten. We generalize Maderâs formulas to totally geodesic Radon transforms in any dimension on arbitrary constant curvature space. Another new interesting inversion formula for the $k$-plane transform was presented in the recent book âIntegral geometry and Radon transformâ by S. Helgason. We extend this formula to arbitrary constant curvature space. The paper combines tools of integral geometry and complex analysis.References
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Additional Information
- Y. A. Antipov
- Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
- MR Author ID: 245270
- Email: antipov@math.lsu.edu
- B. Rubin
- Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
- MR Author ID: 209987
- Email: borisr@math.lsu.edu
- Received by editor(s): March 10, 2011
- Published electronically: June 12, 2012
- Additional Notes: The first author was supported by the NSF grant DMS-0707724.
The second author was supported by the NSF grants PFUND-137 (Louisiana Board of Regents) and DMS-0556157. - © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 364 (2012), 6479-6493
- MSC (2010): Primary 44A12; Secondary 47G10
- DOI: https://doi.org/10.1090/S0002-9947-2012-05643-1
- MathSciNet review: 2958944