On Fourier Transforms of Radial Functions and Distributions
نویسنده
چکیده
We find a formula that relates the Fourier transform of a radial function on R with the Fourier transform of the same function defined on R. 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 7→ f(|t|) and the two-dimensional function (x1, x2) 7→ f(|(x1, x2)|). We prove analogous results for radial tempered distributions.
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تاریخ انتشار 2012