Publication Cover
Applicable Analysis
An International Journal
Volume 83, 2004 - Issue 5
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Original Articles

Quasi-exchange Formulas for Wavelet Transforms of Distributions

Pages 501-507 | Received 07 Jul 2003, Published online: 07 Oct 2011
 

Abstract

We investigate the wavelet transforms of tempered distributions in a way that closely links their Fourier transforms and wavelet transforms. Two exchange formulas of the convolution and the multiplication of wavelet transforms of tempered distributions are established. We call these formulas the quasi-exchange formulas for wavelet transforms of distributions, because of the resemblance between these formulas and the well-known exchange formula for Fourier transforms.

Acknowledgement

The author is grateful to the referee for helpful comments.

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