Characterization of low pass filters in a multiresolution analysis

A. San Antolín. "Characterization of low pass filters in a multiresolution analysis." Studia Mathematica 190.2 (2009): 99-116. <http://eudml.org/doc/285022>.

@article{A2009,
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: 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.},
author = {A. San Antolín},
journal = {Studia Mathematica},
keywords = {approximate continuity; filter multiplier; Fourier transform; low pass filter; multiresolution analysis},
language = {eng},
number = {2},
pages = {99-116},
title = {Characterization of low pass filters in a multiresolution analysis},
url = {http://eudml.org/doc/285022},
volume = {190},
year = {2009},
}

TY - JOUR
AU - A. San Antolín
TI - Characterization of low pass filters in a multiresolution analysis
JO - Studia Mathematica
PY - 2009
VL - 190
IS - 2
SP - 99
EP - 116
AB - 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.
LA - eng
KW - approximate continuity; filter multiplier; Fourier transform; low pass filter; multiresolution analysis
UR - http://eudml.org/doc/285022
ER -