Characterization of low pass filters in a multiresolution analysis

Volume 190 / 2009

A. San Antolín Studia Mathematica 190 (2009), 99-116 MSC: Primary 42C40; Secondary 47B38, 42B15, 42B35, 28A33. DOI: 10.4064/sm190-2-1


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.


  • A. San AntolínDepartamento de Matemáticas
    Universidad Autónoma de Madrid
    28049 Madrid, Spain

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