On the orthogonality of a system of shifts of the scaling function on Vilenkin groups
type: Item
instance of: scholarly article
title: On the orthogonality of a system of shifts of the scaling function on Vilenkin groups
zbMATH Open document ID: 1365.43007
DOI: 10.1134/S000143461507038X
author: S. F. Lukomskii
author: G. S. Berdnikov
author: Yu. S. Kruss
published in: Mathematical Notes
publication date: 2015-10-26T00:00:00Z
review text: This short paper is concerned with the problem of constructing an orthogonal scaling function and of avoiding the exhaustive search. The authors reduce the problem of constructing such a function to determining a graph that could be constructed from an arbitrary \(N\)-valid tree. The main result of the paper is the Theorem, just before the end of the paper. It was considered for different \(N\) and \(p\) by the authors in a succesive order until they were able to obtain it for arbitrary \(N\) and \(p\).
reviewed by: Darian Onchis-Moaca
Mathematics Subject Classification ID: 43A70
Mathematics Subject Classification ID: 42C10
zbMATH DE Number: 6498272
zbMATH Keywords: orthogonal MRA
zbMATH Keywords: Vilenking group
zbMATH Keywords: scaling function
zbMATH Keywords: exhaustive search problem
zbMATH Keywords: N-valid tree
zbMATH Keywords: step-function
MaRDI profile type: Publication
cites work: N-Valid trees in wavelet theory on Vilenkin groups
cites work: Step refinable functions and orthogonal MRA on Vilenkin groups
full work available at URL: s000143461507038x
OpenAlex ID: W2302356378
description: scientific article; zbMATH DE number 6498272