Decay Estimates of High Dimensional Adjoint Radon Transforms

2023/10/24 by Ruipeng Shen, Shen, Ruipeng
Mathematics · Medicine · #35L05 #44A12 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Medical Imaging Techniques and Applications #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2310.15843

openalex publication_date 2023/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove an optimal L²-L^2d decay estimate of the adjoint Radon transform of compactly supported data in d-dimensional space via a geometric method. A similar problem in dimension 3 has be considered in the author's previous work. This work deals with all higher dimensional case d≥ 4. As an application we give the decay of Strichartz norms of 5-dimensional non-radiative free waves. The general idea is similar to the lower dimensional case but we introduce a new method to prove the corresponding geometric inequality because the old method becomes too complicated in higher dimensions.

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