The Fourier transform of multiradial functions

Abstract

We obtain an exact formula for the Fourier transform of multiradial functions, i.e., functions of the form $\Phi (x)=\varphi (|x_1|,\dots ,|x_m|)$, $x_i\in {\mathbf{R}}^{n_i}$, in terms of the Fourier transform of the function $\varphi$ on ${\mathbf{R}}^{r_1}\times \cdots \times {\mathbf{R}}^{r_m}$, where $r_i$ is either 1 or 2.

14 pages

References in corpus (1)

• On Fourier transforms of radial functions and distributions