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Large classes of minimally supported frequency wavelets ofL 2(ℝ) andH 2(ℝ)

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Abstract

We introduce a new method to construct large classes of minimally supported frequency (MSF) wavelets of the Hardy space H 2(ℝ)and symmetric MSF wavelets of L 2(ℝ),and discuss the classification of such wavelets. As an application, we show that there are uncountably many such wavelet sets of L 2(ℝ)and H 2 (ℝ).We also enumerate some of the symmetric wavelet sets of L 2 (ℝ)and all wavelet sets of H 2(ℝ)consisting of three intervals. Finally, we construct families of MSF wavelets of L 2 (ℝ)with Fourier transform even and not vanishing in any neighborhood of the origin.

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Authors and Affiliations

  1. Department of Mathematics, University of Bologna, Piazza di Porta San Donata 5, 40127, Italy

    Nicola Arcozzi

  2. Department of Mathematics, Indian Institute of Technology, 208016, Kanpur, India

    Biswaranjan Behera

  3. Statistics and Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, 700108, Calcutta, India

    Biswaranjan Behera

  4. Department of Mathematics, Indian Institute of Technology, 208016, Kanpur, India

    Shobha Madan

Authors
  1. Nicola Arcozzi
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  2. Biswaranjan Behera
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  3. Shobha Madan
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Arcozzi, N., Behera, B. & Madan, S. Large classes of minimally supported frequency wavelets ofL 2(ℝ) andH 2(ℝ). J Geom Anal 13, 557–579 (2003). https://doi.org/10.1007/BF02921878

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  • DOI: https://doi.org/10.1007/BF02921878

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