On Fourier transforms of radial functions and distributions

Abstract

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.

12 pages

References in corpus (1)

• Weyl-Titchmarsh Theory for Schroedinger Operators with Strongly Singular Potentials

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