Trees in Wavelet analysis on Vilenkin groups

Abstract

We consider a class of (1, M )-elementary step functions on the p-adic Vilenkin group. We prove that (1, M )-elementary step function generates a MRA on p-adic Vilenkin group iff it is generated by a rooted tree on the set of vertices {0, 1, . . . p−1} with 0 as a root. Bibliography: 14 titles.