J. Fourier Anal. Appl. 19, 167-179 (2013) [DOI: 10.1007/s00041-012-9242-5]

On Fourier transforms of radial functions and distributions

Loukas Grafakos and Gerald Teschl

We find a formula that relates the Fourier transform of a radial function on n with the Fourier transform of the same function defined on n+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.

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

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