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

 

A generalization of the Mader-Helgason inversion formulas for Radon transforms


Authors: Y. A. Antipov and B. Rubin
Journal: Trans. Amer. Math. Soc. 364 (2012), 6479-6493
MSC (2010): Primary 44A12; Secondary 47G10
Published electronically: June 12, 2012
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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 Mader's 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 ``Integral geometry and Radon transform'' by S. Helgason. We extend this formula to arbitrary constant curvature space. The paper combines tools of integral geometry and complex analysis.


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Additional Information

Y. A. Antipov
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email: antipov@math.lsu.edu

B. Rubin
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email: borisr@math.lsu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05643-1
PII: S 0002-9947(2012)05643-1
Keywords: Radon transforms, inversion formulas, constant curvature space.
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.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.