The Fourier transform of multiradial functions

2013/07/31 by Frederic Bernicot, Frédéric Bernicot, Bernicot, Frederic +4
Mathematics · #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical Analysis and Transform Methods #math.CA

paper · pdf · doi:10.48550/arxiv.1307.8408

14 pages

arxiv created 2013/07/31 · openalex publication_date 2013/07/31 · arxiv updated 2013/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain an exact formula for the Fourier transform of multiradial functions, i.e., functions of the form Φ(x)=ϕ(|x₁|, …, |x_m|), x_i∈ \mathbf R^n_i, in terms of the Fourier transform of the function ϕ on \mathbf R^r₁× ⋯ × \mathbf R^r_m, where r_i is either 1 or 2.

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