A note on the convolution theorem for the Fourier transform

被引：0
|
作者：
Charles S. Kahane
机构：
[1] Vanderbilt University,Department of Mathematics
来源：
Czechoslovak Mathematical Journal | 2011年 / 61卷
关键词：
convolution; Fourier transform; 42A38; 39B22;
D O I：
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学科分类号：
摘要：
In this paper we characterize those bounded linear transformations Tf carrying L1(ℝ1) into the space of bounded continuous functions on ℝ1, for which the convolution identity T(f * g) = Tf · Tg holds. It is shown that such a transformation is just the Fourier transform combined with an appropriate change of variable.
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页码：199 / 207
页数：8
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