A note on the linear independence of characteristic functions of self-similar sets
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.
scientific article; zbMATH DE number 937072