1112.5469 (Loukas Grafakos et al.)

On Fourier transforms of radial functions and distributions    [PDF]

Loukas Grafakos, Gerald Teschl

We find a formula that relates the Fourier transform of a radial function on $\mathbf{R}^n$ with the Fourier transform of the same function defined on $\mathbf{R}^{n+2}$. 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 $t\to f(|t|)$ and the two-dimensional function $(x_1,x_2)\to f(|(x_1,x_2)|)$. We prove analogous results for radial tempered distributions.

View original: http://arxiv.org/abs/1112.5469