Article
J. Fourier Anal. Appl. (to appear)

On Fourier transforms of radial functions and distributions

Loukas Grafakos and Gerald Teschl

Abstract
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\mapsto f(|t|) and the two-dimensional function (x1,x2)\mapsto f(|(x1,x2)|). We prove analogous results for radial tempered distributions.

MSC2010: Primary 42B10, 42A10; Secondary 42B37
Keywords: Radial Fourier transform, Hankel transform

Download
TeX file (32K) or pdf file (308K)