Elementary Inversion of Riesz Potentials and Radon-John Transforms
Boris Rubin
TL;DR
This paper presents new simple proofs for elementary inversion formulas of Riesz potentials and applies these results to reconstruct functions from their integrals over Euclidean planes in integral geometry.
Contribution
It introduces simplified proofs for inversion formulas of Riesz potentials and applies them to function reconstruction from plane integrals in integral geometry.
Findings
Simplified proofs for Riesz potential inversion formulas
Application to function reconstruction from plane integrals
Enhanced understanding of integral geometric methods
Abstract
New simple proofs are given to some elementary approximate and explicit inversion formulas for Riesz potentials. The results are applied to reconstruction of functions from their integrals over Euclidean planes in integral geometry.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Mathematical functions and polynomials · Numerical methods in inverse problems