Non-Haar MRA on local fields of positive characteristic

Abstract

We propose a simple method to construct integral periodic mask and corresponding scaling step functions that generate non-Haar orthogonal MRA on the local field $ F^{(s)}$ of positive characteristic $p$. To construct this mask we use two new ideas. First, we consider local field as vector space over the finite field $GF(p^s)$. Second, we construct scaling function by arbitrary tree that has $p^s$ vertices. By fixed prime number $p$ there exist $p^{s(p^s-2)}$ such trees.