WAVELET ANALYSIS ON THE CANTOR DYADIC GROUP

Abstract

ABSTRACT. Compactly supported orthogonal wavelets are built on the Can-tor dyadic group (the dyadic or a-series local field). Necessary and sufficient conditions are given on a trigonometric polynomial scaling filter for a mul-tiresolution analysis to result. A Lipschitz regularity condition is defined and an unconditional P-convergence result is given for regular wavelet ex-pansions (p> 1). Wavelets are given whose scaling filter is a trigonometric polynomial with 2n many terms; regular wavelets with filters with 8 terms are detailed. These wavelets are identified with certain Walsh series on the real line. A Mallat tree algorithm is given for the wavelets. 1.