A Class of non-MRA Band-limited Wavelets

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We give a characterization of a class of band-limited wavelets of $L^2({\mathbb R})$ and show that none of these wavelets come from a multiresolution analysis (MRA). For each $n\geq 2$, we construct a subset $S_n$ of ${\mathbb R}$ which is symmetric with respect to the origin. We give necessary and sufficient conditions on a function $ψ\in L^2({\mathbb R})$ with supp $\hatψ\subseteq S_n$ to be an orthonormal wavelet. This result generalizes the characterization of a class of wavelets of E. Hernández and G. Weiss. The dimension functions associated with these wavelets are also computed explicitly. Starting from the wavelets we have constructed, we are able to construct examples of wavelets in each of the equivalence classes of wavelets defined by E. Weber.
AMS Latex, 17 pages

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Functional Analysis, 42C40

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http://salesiana.dossiersoluciones.com/handle/123456789/62031

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0108114
 http://arxiv.org/abs/math/0108114
 Section 6 is published as "Wavelet subspaces invariant under groups of translation operators, Proc. Indian Acad. Sci. Math. Sci., Vol. 113, No. 2 (2003), pp. 171-178."

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