Overdetermined Transforms in Integral Geometry

2013/11/29 by Boris Rubin, Rubin, Boris
Engineering · Mathematics · Medicine · #44A12 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Medical Imaging Techniques and Applications #math.FA #msc:44A12

paper · pdf · doi:10.48550/arxiv.1311.7678

27 pages

arxiv created 2013/11/29 · openalex publication_date 2013/11/29 · arxiv updated 2013/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A simple example of an n-dimensional admissible complex of planes is given for the overdetermined k-plane transform in ℝⁿ. For the corresponding restricted k-plane transform sharp existence conditions are obtained and explicit inversion formulas are discussed in the general context of L^p functions. Similar questions are studied for overdetermined Radon type transforms on the sphere and the hyperbolic space. A theorem describing the range of the restricted k-plane transform on the space of rapidly decreasing smooth functions is proved.

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• Revisiting the Problem of Recovering Functions in \Bbb Rⁿ by Integration on k Dimensional Planes
• L^p - L^p' estimates for overdetermined Radon transforms
• Sufficient Conditions for the Inversion Formula for the k-plane Radon Transform in Rⁿ
• Radon Transforms for Mutually Orthogonal Affine Planes
• The Generalized Mader's Inversion Formulas for the Radon Transforms