Ray Transforms and Vector Fields

2011/02/08 by Nicholas Hoell, Hoell, Nicholas
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1102.1736

openalex publication_date 2011/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We review and extend a technique for recovering a smooth function from its averages over a wide class of curves in a general region of Euclidean space. The method is based on complexification of the underlying vector fields defining the transport and recasting the problem in terms of complex-analytic function theory. Conditions on the validity of prior formulae appearing in a previous paper as well as stability estimates are then discussed first for the case of vector fields with polynomial coefficients and later for more general cases.

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