Large classes of minimally supported frequency wavelets of L²(\R) and H²(\R)

2002/07/17 by Nicola Arcozzi, Biswaranjan Behera, Shobha Madan
Mathematics · #math.FA #msc:42C40

paper · pdf

published as J. Geom. Anal., vol. 13, no. 4, (2003) pp. 557-579. · 28 pages

arxiv created 2002/07/17 · arxiv updated 2009/11/30

Abstract

We introduce a method to construct large classes of MSF wavelets of the Hardy space H²(\R) and symmetric MSF wavelets of L²(\R), and discuss the classification of such sets. As application, we show that there are uncountably many wavelet sets of L²(\R) and H²(\R). We also enumerate all symmetric wavelets of L²(\R) with at most three intervals in the positive axis as well as 3-interval wavelet sets of H²(\R). Finally, we construct families of MSF wavelets of L²(\R) whose Fourier transform does not vanish in any neighbourhood of the origin.

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