The Inverse Problem for the Euler-Poisson-Darboux Equation and Shifted k-Plane Transforms

2022/12/21 by Boris Rubin, Rubin, Boris
Computer Science · Mathematics · #35R30 #42B15 #44A12 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2212.11179

openalex publication_date 2022/12/21 · openalex created_date 2023/01/04 · openalex updated_date 2026/07/28

Abstract

The inverse problem for the Euler-Poisson-Darboux equation deals with reconstruction of the Cauchy data for this equation from incomplete information about its solution. In the present article, this problem is studied in connection with the injectivity of the shifted k-plane transform, which assigns to functions in L^p(\mathbb Rⁿ) their mean values over all k-planes at a fixed distance from the given k-planes. Several generalizations, including the Radon transform over strips of fixed width in \mathbb R² and a similar transform over tubes of fixed diameter in \mathbb R³, are considered.

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