Characterization of low pass filters in a multiresolution analysis

@article{Antoln2009CharacterizationOL,
  title={Characterization of low pass filters in a multiresolution analysis},
  author={A. S. Antol{\'i}n},
  journal={Studia Mathematica},
  year={2009},
  volume={190},
  pages={99-116}
}
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 : R → R such that A(Z) ⊂ Z 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… Expand
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