Trees in Wavelet analysis on Vilenkin groups

2013/03/22 by С. Ф. Лукомский, Lukomskii, S. F.
Computer Science · Mathematics · #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.1303.5635

openalex publication_date 2013/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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