Smooth orthonormal wavelets with exponential decay in both time and frequency domains

Abstract

This article presents the existence of a non-trivial smooth orthonormal wavelet with exponential decay in both time and frequency domains. Meanwhile, we also show that the Meyer wavelets are not in the Schwartz class.

Keywords:

• Orthonormal wavelets
• Exponential decay
• Schwartz class

Keywords:

• 2000 Mathematics Subject Classification:
• 42C4O

Acknowledgment

The authors would like to thank Professor Der-Chen Chang for his valuable comments.