The Radon Transform on the Heisenberg Group and the Transversal Radon Transform

2009/10/13 by Boris Rubin, Rubin, Boris
Mathematics · Medicine · #44A12 #47G10 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Medical Imaging Techniques and Applications #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.0910.2312

openalex publication_date 2009/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The notion of the Radon transform on the Heisenberg group was introduced by R. Strichartz and inspired by D. Geller and E.M. Stein's related work. The more general transversal Radon transform integrates functions on the m-dimensional real Euclidean space over hyperplanes meeting the last coordinate axis. We obtain new boundedness results and explicit inversion formulas for both transforms on L^p functions in the full range of the parameter p. We also show that these transforms are isomorphisms of the corresponding Semyanistyi-Lizorkin spaces of smooth functions. In the framework of these spaces we obtain inversion formulas, which are pointwise analogues of the corresponding formulas by R. Strichartz.

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