Large classes of minimally supported frequency wavelets of L^2(\R) and H^2(\R)

Details Large classes of minimally supported frequency wavelets of L^2(\R) and H^2(\R) Large classes of minimally supported frequency wavelets of L^2(\R) and H^2(\R)

2002-07-17

arxiv.org/abs/math/0207141v1

J. Geom. Anal., vol. 13, no. 4, (2003) pp. 557-579.

Mathematics

Functional Analysis

28 pages

Scientific paper

We introduce a method to construct large classes of MSF wavelets of the Hardy space H^2(\R) and symmetric MSF wavelets of L^2(\R), and discuss the classification of such sets. As application, we show that there are uncountably many wavelet sets of L^2(\R) and H^2(\R). We also enumerate all symmetric wavelets of L^2(\R) with at most three intervals in the positive axis as well as 3-interval wavelet sets of H^2(\R). Finally, we construct families of MSF wavelets of L^2(\R) whose Fourier transform does not vanish in any neighbourhood of the origin.

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