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: ℝⁿ → ℝⁿ such that A(ℤⁿ) ⊂ ℤⁿ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm190-2-1,
author = {A. San Antol\'\i n},
title = {Characterization of low pass filters in a multiresolution analysis},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {99-116},
zbl = {1166.42022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm190-2-1}
}
A. San Antolín. Characterization of low pass filters in a multiresolution analysis. Studia Mathematica, Tome 192 (2009) pp. 99-116. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm190-2-1/