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The Fourier transform of multiradial functions |
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| Authors: | Frédéric Bernicot Loukas Grafakos Yandan Zhang |
| Institution: | 1. Laboratoire Jean Leray, CNRS, Université de Nantes, 2, rue de la Houssinière, 44322?, Nantes cedex 3, France 2. Department of Mathematics, University of Missouri, Columbia, MO, 65211, USA 3. Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou, Zhejiang, China |
| Abstract: | We obtain an exact formula for the Fourier transform of multiradial functions, i.e., functions of the form \(\varPhi (x)=\phi (|x_1|, \dots , |x_m|), x_i\in \mathbf R^{n_i}\) , in terms of the Fourier transform of the function \(\phi \) on \(\mathbf R^{r_1}\times \cdots \times \mathbf R^{r_m}\) , where \(r_i\) is either \(1\) or \(2\) . |
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