We give a characterization of biorthogonal wavelets arising from MRA's of multiplicity D entirely in terms of the dimension function. This improves the previous characterization in [8] removing an unnecessary angle condition. Besides we characterize Riesz wavelets arising from MRA's, and present new proofs based on shift-invariant space theory, generalizing the 1-dimensional results appearing in [17].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm160-3-3,
author = {Marcin Bownik and Gustavo Garrig\'os},
title = {Biorthogonal wavelets, MRA's and shift-invariant spaces},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {231-248},
zbl = {1053.42029},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm160-3-3}
}
Marcin Bownik; Gustavo Garrigós. Biorthogonal wavelets, MRA's and shift-invariant spaces. Studia Mathematica, Tome 162 (2004) pp. 231-248. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm160-3-3/