Affine frames, GMRA's, and the canonical dual

Marcin Bownik, and Eric Weber. "Affine frames, GMRA's, and the canonical dual." Studia Mathematica 159.3 (2003): 453-479. <http://eudml.org/doc/285042>.

@article{MarcinBownik2003,
abstract = {We show that if the canonical dual of an affine frame has the affine structure, with the same number of generators, then the core subspace V₀ is shift invariant. We demonstrate, however, that the converse is not true. We apply our results in the setting of oversampling affine frames, as well as in computing the period of a Riesz wavelet, answering in the affirmative a conjecture of Daubechies and Han. Additionally, we completely characterize when the canonical dual of a quasi-affine frame has the quasi-affine structure.},
author = {Marcin Bownik, Eric Weber},
journal = {Studia Mathematica},
keywords = {affine frames; wavelet frames; canonical dual frames; Riesz basis; shift invariant spaces},
language = {eng},
number = {3},
pages = {453-479},
title = {Affine frames, GMRA's, and the canonical dual},
url = {http://eudml.org/doc/285042},
volume = {159},
year = {2003},
}

TY - JOUR
AU - Marcin Bownik
AU - Eric Weber
TI - Affine frames, GMRA's, and the canonical dual
JO - Studia Mathematica
PY - 2003
VL - 159
IS - 3
SP - 453
EP - 479
AB - We show that if the canonical dual of an affine frame has the affine structure, with the same number of generators, then the core subspace V₀ is shift invariant. We demonstrate, however, that the converse is not true. We apply our results in the setting of oversampling affine frames, as well as in computing the period of a Riesz wavelet, answering in the affirmative a conjecture of Daubechies and Han. Additionally, we completely characterize when the canonical dual of a quasi-affine frame has the quasi-affine structure.
LA - eng
KW - affine frames; wavelet frames; canonical dual frames; Riesz basis; shift invariant spaces
UR - http://eudml.org/doc/285042
ER -