Fractal multiwavelets related to the cantor dyadic group

Abstract

Orthogonal wavelets on the Cantor dyadic group are identified with multiwavelets on the real line consisting of piecewise fractal functions. A tree algorithm for analysis using these wavelets is described. Multiwavelet systems with algorithms of similar structure include certain orthogonal compactly supported multiwavelets in the linear double-knot spline space S1,2.

Keywords

• Wavelets
• multiwavelets
• fractal functions
• Cantor dyadic group
• splines.