2001/08/16 by Biswaranjan Behera, Shobha Madan
Mathematics · #math.FA #msc:42C40
published as 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." · AMS Latex, 17 pages
arxiv created 2001/08/16 · arxiv updated 2009/11/30
We give a characterization of a class of band-limited wavelets of L2(\mathbb R) and show that none of these wavelets come from a multiresolution analysis (MRA). For each n≥ 2, we construct a subset Sn of \mathbb R which is symmetric with respect to the origin. We give necessary and sufficient conditions on a function ψ∈ L2(\mathbb R) with supp ψ⊆ Sn 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.