On Fourier Transforms of Radial Functions and Distributions

@article{Grafakos2013OnFT,
  title={On Fourier Transforms of Radial Functions and Distributions},
  author={Loukas Grafakos and Gerald Teschl},
  journal={Journal of Fourier Analysis and Applications},
  year={2013},
  volume={19},
  pages={167-179}
}
  • L. GrafakosG. Teschl
  • Published 22 December 2011
  • Mathematics
  • Journal of Fourier Analysis and Applications
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. 

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