Quasi-exchange Formulas for Wavelet Transforms of Distributions

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.

Keywords:

• Wavelet transforms of distributions
• Quasi-exchange formula
• AMS Subject Classification: 46F12
• 42A85
• 44A35
• 43A65

Acknowledgement

The author is grateful to the referee for helpful comments.