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Original Articles

Convolution and Fourier transform over the spaces

Pages 377-391 | Received 01 Mar 2012, Accepted 19 May 2012, Published online: 29 Jun 2012
 

Abstract

We define convolution of two distributions in the spaces , in two ways, which turn out to be equivalent, and show that the space is closed under convolution. We also define the Fourier transform of elements of , and prove the Parseval equality.

2000 AMS Subject Classifications :

Acknowledgements

I thank the referee for pointing out to me Citation6–9 and for his comments which helped improving an earlier version of the paper.

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