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Single wavelets in n-dimensions

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Abstract

Under very minimal regularity assumptions, it can be shown that 2n−1 functions are needed to generate an orthonormal wavelet basis for L2(ℝn). In a recent paper by Dai et al. it is shown, by abstract means, that there exist subsets K of ℝn such that the single function ψ, defined by\(\hat \psi = \chi K\), is an orthonormal wavelet for L2(ℝn). Here we provide methods for construucting explicit examples of these sets. Moreover, we demonstrate that these wavelets do not behave like their one-dimensional couterparts.

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Authors and Affiliations

  1. Dipartimento di Matematica, via Saldini 50, 20133, Milano, Italy

    Paolo M. Soardi

  2. Department of Mathematics, University of Texas at Austin, 78712, Austin, TX

    David Weiland

Authors
  1. Paolo M. Soardi
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  2. David Weiland
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Communicated by John. Benedetto

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Soardi, P.M., Weiland, D. Single wavelets in n-dimensions. The Journal of Fourier Analysis and Applications 4, 299–315 (1998). https://doi.org/10.1007/BF02476029

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  • DOI: https://doi.org/10.1007/BF02476029

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