Journal of Fourier Analysis and Applications

, Volume 19, Issue 1, pp 167–179

On Fourier Transforms of Radial Functions and Distributions

Article

DOI: 10.1007/s00041-012-9242-5

Cite this article as:
Grafakos, L. & Teschl, G. J Fourier Anal Appl (2013) 19: 167. doi:10.1007/s00041-012-9242-5

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 tf(|t|) and the two-dimensional function (x1,x2)↦f(|(x1,x2)|). We prove analogous results for radial tempered distributions.

Keywords

Radial Fourier transformHankel transform

Mathematics Subject Classification (2000)

42B1042A1042B37

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MissouriColumbiaUSA
  2. 2.Faculty of MathematicsUniversity of ViennaWienAustria
  3. 3.International Erwin Schrödinger Institute for Mathematical PhysicsWienAustria