Examples of wavelets for local fields
Abstract
Description
Using the wavelet theory introduced by the author and J. Benedetto, we present examples of wavelets on p-adic fields and other locally compact abelian groups with compact open subgroups. We observe that in this setting, the Haar and Shannon wavelets (which are at opposite extremes over the real numbers) coincide and are localized both in time and in frequency. We also study the behavior of the translation operators required in the theory.
21 pages; LaTeX2e; to appear in the proceedings of the AMS Special Session on Wavelets, Frames, and Operator Theory held at Baltimore, January 2003
21 pages; LaTeX2e; to appear in the proceedings of the AMS Special Session on Wavelets, Frames, and Operator Theory held at Baltimore, January 2003