Non-MSF Wavelets for the Hardy Space $H^2({\Bbb R})$

Volume 52 / 2004

Biswaranjan Behera 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.

Authors

  • Biswaranjan BeheraStatistics and Mathematics Unit
    Indian Statistical Institute
    203, B. T. Road
    Calcutta 700108, India
    e-mail

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