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We find a formula that relates the Fourier transform of a radial function on $\mathbf{R}^n$ with the Fourier transform of the same function defined on $\mathbf{R}^{n+2}$.
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A. Kostenko, A. Sakhnovich, and G. Teschl, Weyl–Titchmarsh theory for Schrödinger operators with strongly singular potentials
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