Sufficient Conditions for the Inversion Formula for the k-plane Radon Transform in R^n
Abstract
Description
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.
17 pages. Mistakes in earlier version corrected. Minor changes in notation. New results and references added
17 pages. Mistakes in earlier version corrected. Minor changes in notation. New results and references added