N-valid trees in wavelet theory on Vilenkin groups

2014/12/01 by G. S. Berdnikov, Berdnikov, G. S., С. Ф. Лукомский +1
Computer Science · Mathematics · #11R56 #42C40 #43A70 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Topological and Geometric Data Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1412.3096

openalex publication_date 2014/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a class of (N,M)-elementary step functions on the p-adic Vilenkin group. We prove that (N,M)-elementary step function generates a MRA on p-adic Vilenkin group iff it is generated by a special N-valid rooted tree on the set of vertices \0,1,… p-1\ with the vector (0,...,0)∈ \mathbb Z^N as a root. Bibliography: 15 titles.

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