Journal of Fourier Analysis and Applications

, Volume 19, Issue 1, pp 167–179

On Fourier Transforms of Radial Functions and Distributions



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.


Radial Fourier transform Hankel transform 

Mathematics Subject Classification (2000)

42B10 42A10 42B37 

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

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