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Abstract

We characterize the low pass filters associated with scaling functions of a multiresolution analysis in a general context, where instead of the dyadic dilation one considers the dilation given by a fixed linear invertible map $A: {\mathbb R}^n\rightarrow {\mathbb R}^n$ such that $A(\mathbb Z^n) \subset \mathbb Z^n$ and all (complex) eigenvalues of $A$ have modulus greater than $1.$ This characterization involves the notion of filter multiplier of such a multiresolution analysis. Moreover, the paper contains a characterization of the measurable functions which are filter multipliers.