Abstract
The stability of the integer translates of a univariate refinable function is characterized in terms of the mask sequence in the corresponding k-scale $(k \geq 2)$ refinement equation. We show that the stability and refinement of some kinds of basis functions lead to a multiresolution analysis in $L^p (\mathbb{R}^s )(1 \leq p \leq \infty ,s \in \mathbb{N})$ based on general lattices. As an application we determine explicitly all those multiresolution analyses in $L^2 (\mathbb{R})$ associated with $(\mathbb{Z},k)$ whose scaling functions are characteristic functions.
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