Non-MSF Wavelets for the Hardy Space $H^2({\Bbb R})$
Volume 52 / 2004
Bulletin Polish Acad. Sci. Math. 52 (2004), 169-178
MSC: Primary 42C40; Secondary 42C15.
DOI: 10.4064/ba52-2-7
Abstract
All wavelets constructed so far for the Hardy space $H^2({\Bbb R})$ are MSF wavelets. We construct a family of $H^2$-wavelets which are not MSF. An equivalence relation on $H^2$-wavelets is introduced and it is shown that the corresponding equivalence classes are non-empty. Finally, we construct a family of $H^2$-wavelets with Fourier transform not vanishing in any neighbourhood of the origin.
