All wavelets constructed so far for the Hardy space H²(ℝ) are MSF wavelets. We construct a family of H²-wavelets which are not MSF. An equivalence relation on H²-wavelets is introduced and it is shown that the corresponding equivalence classes are non-empty. Finally, we construct a family of H²-wavelets with Fourier transform not vanishing in any neighbourhood of the origin.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-2-7,
author = {Biswaranjan Behera},
title = {Non-MSF Wavelets for the Hardy Space H$^2$($\mathbb{R}$)},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {52},
year = {2004},
pages = {169-178},
zbl = {1096.42023},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-2-7}
}
Biswaranjan Behera. Non-MSF Wavelets for the Hardy Space H²(ℝ). Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) pp. 169-178. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-2-7/