Biorthogonal Wavelets on Local Fields of Positive Characteristic

Abstract

We generalize the concept of biorthogonal wavelets to a local field $K$ of positive characteristic. We show that if the translates of the scaling functions of two multiresolution analyses are biorthogonal, then the associated wavelet families are also biorthogonal. Under mild assumptions on the scaling functions and the wavelets, we also show that the wavelets generate Riesz bases for $L^2(K)$.