# On Fourier Transforms of Radial Functions and Distributions

@article{Grafakos2013OnFT,
title={On Fourier Transforms of Radial Functions and Distributions},
author={Loukas Grafakos and Gerald Teschl},
journal={Journal of Fourier Analysis and Applications},
year={2013},
volume={19},
pages={167-179}
}
• Published 2013
• Mathematics, Physics
• Journal of Fourier Analysis and Applications
We find a formula that relates the Fourier transform of a radial function on Rn with the Fourier transform of the same function defined on Rn+2. This formula enables one to explicitly calculate the Fourier transform of any radial function f(r) in any dimension, provided one knows the Fourier transform of the one-dimensional function t↦f(|t|) and the two-dimensional function (x1,x2)↦f(|(x1,x2)|). We prove analogous results for radial tempered distributions.
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