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

Y. A. Antipov; B. Rubin

doi:10.1090/S0002-9947-2012-05643-1

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

Y. A. Antipov
, B. Rubin

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

In 1927, Philomena Mader derived elegant inversion formulas for the hyperplane Radon transform on 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.

Original language	English
Pages (from-to)	6479-6493
Number of pages	15
Journal	Transactions of the American Mathematical Society
Volume	364
Issue number	12
DOIs	https://doi.org/10.1090/S0002-9947-2012-05643-1
State	Published - 2012
Externally published	Yes

Keywords

Constant curvature space
Inversion formulas
Radon transforms

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10.1090/S0002-9947-2012-05643-1

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abstract = "In 1927, Philomena Mader derived elegant inversion formulas for the hyperplane Radon transform on 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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A generalization of the Mader-Helgason inversion formulas for radon transforms

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Keywords

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