A note on the convolution theorem for the Fourier transform

被引：0
|
作者：
Kahane, Charles S. [1 ]
机构：
[1] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA
来源：
CZECHOSLOVAK MATHEMATICAL JOURNAL | 2011年 / 61卷 / 01期
关键词：
convolution; Fourier transform;
D O I：
10.1007/s10587-011-0006-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we characterize those bounded linear transformations Tf carrying L (1)(a"e(1)) into the space of bounded continuous functions on a"e(1), for which the convolution identity T(f * g) = Tf center dot Tg holds. It is shown that such a transformation is just the Fourier transform combined with an appropriate change of variable.
引用
收藏
页码：199 / 207
页数：9
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