Non-Haar MRA on local fields of positive characteristic

2014/07/15 by Lukomskii, Sergey, Vodolazov, Alexander
#FOS: Mathematics #Number Theory (math.NT) #Primary 42C40 #Secondary 43A70

paper · doi:10.48550/arxiv.1407.4069

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(ps-2) such trees.

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