Sufficient Conditions for the Inversion Formula for the k-plane Radon Transform in R^n

Details Sufficient Conditions for the Inversion Formula for the k-plane Radon Transform in R^n Sufficient Conditions for the Inversion Formula for the k-plane Radon Transform in R^n

2002-08-16

arxiv.org/abs/math/0208129v2

Mathematics

Classical Analysis and ODEs

17 pages. Mistakes in earlier version corrected. Minor changes in notation. New results and references added

Scientific paper

The inversion theorem for the k-plane Radon transform in R^n is often stated for Schwartz functions, and lately for smooth functions on R^n fulfilling that f(x)=O(|x|^{-N}) for some N>n. In this paper it will be shown, that it suffices to require that f is locally Holder continuous and f(x)=O(|x|^{-N}) for some N>k (N not necessarily an integer), and that a slightly weaker inversion formula holds when f with the same decay as before is only continuous.

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