A note on the convolution theorem for the Fourier transform

Title:

A note on the convolution theorem for the Fourier transform

Creator:

Kahane, Charles S.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:0dfff23b-a83f-47bf-ad83-27234ed74e2a
uuid:0dfff23b-a83f-47bf-ad83-27234ed74e2a

Subject:

convolution and Fourier transform

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In this paper we characterize those bounded linear transformations $Tf$ carrying $L^{1}( \mathbb {R}^{1}) $ into the space of bounded continuous functions on $\mathbb {R}^{1}$, for which the convolution identity $T(f\ast g) =Tf\cdot Tg $ holds. It is shown that such a transformation is just the Fourier transform combined with an appropriate change of variable.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

199-207

Source:

Czechoslovak Mathematical Journal | 2011 Volume:61 | Number:1

Harvested from:

CDK

Metadata only:

false