On Fourier Transforms of Radial Functions and Distributions
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↦f(|t|) and the two-dimensional function (x1,x2)↦f(|(x1,x2)|). We prove analogous results for radial tempered distributions.
- Publication:
-
Journal of Fourier Analysis and Applications
- Pub Date:
- February 2013
- DOI:
- arXiv:
- arXiv:1112.5469
- Bibcode:
- 2013JFAA...19..167G
- Keywords:
-
- Radial Fourier transform;
- Hankel transform;
- 42B10;
- 42A10;
- 42B37;
- Mathematics - Classical Analysis and ODEs;
- Mathematical Physics;
- Mathematics - Analysis of PDEs;
- 42B10;
- 42A10 (Primary) 42B37 (Secondary)
- E-Print:
- 12 pages