The Fourier transform of multiradial functions

被引：0
作者：
Frédéric Bernicot
Loukas Grafakos
Yandan Zhang
机构：
[1] Laboratoire Jean Leray,Department of Mathematics
[2] CNRS,Department of Mathematics
[3] Université de Nantes,undefined
[4] University of Missouri,undefined
[5] Zhejiang University of Science and Technology,undefined
来源：
Monatshefte für Mathematik | 2014年 / 175卷
关键词：
Multiradial function; Fourier transform; 42B10; 42B37;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We obtain an exact formula for the Fourier transform of multiradial functions, i.e., functions of the form Φ(x)=ϕ(|x1|,⋯,|xm|),xi∈Rni\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varPhi (x)=\phi (|x_1|, \dots , |x_m|), x_i\in \mathbf R^{n_i}$$\end{document}, in terms of the Fourier transform of the function ϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi $$\end{document} on Rr1×⋯×Rrm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf R^{r_1}\times \cdots \times \mathbf R^{r_m}$$\end{document}, where ri\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r_i$$\end{document} is either 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1$$\end{document} or 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2$$\end{document}.
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页码：43 / 64
页数：21
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