A note on the linear independence of characteristic functions of self-similar sets
type: Item
instance of: scholarly article
title: A note on the linear independence of characteristic functions of self-similar sets
zbMATH Open document ID: 0854.28002
DOI: 10.1007/BF01323986
author: Stephan Dahlke
author: Vera Latour
published in: Archiv der Mathematik
publication date: 1996-10-20T00:00:00Z
review text: Specific self-similar sets in \(\mathbb{R}^n\) with respect to an expanding integer scaling matrix have applications in wavelet analysis. In this paper, we give necessary and sufficient conditions for the linear independence of the translates of the characteristic functions associated with these sets. Furthermore, we show that for specific scaling matrices these conditions can be checked directly from the representers of certain equivalence classes induced by the scaling matrix.
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 41A30
zbMATH DE Number: 937072
zbMATH Keywords: stability
zbMATH Keywords: refinable functions
zbMATH Keywords: expanding scaling matrices
zbMATH Keywords: self-similar sets
zbMATH Keywords: linear independence
zbMATH Keywords: characteristic functions
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01323986
OpenAlex ID: W2074235133
description: scientific article; zbMATH DE number 937072