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Orthogonal Polynomial Wavelets

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Abstract

Recently Fischer and Prestin presented a unified approach for the construction of polynomial wavelets. In particular, they characterized those parameter sets which lead to orthogonal scaling functions. Here, we extend their results to the wavelets. We work out necessary and sufficient conditions for the wavelets to be orthogonal to each other. Furthermore, we show how these computable characterizations lead to attractive decomposition and reconstruction schemes. The paper concludes with a study of the special case of Bernstein–Szegö weight functions.

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Authors and Affiliations

  1. Institute of Mathematics, Medical University of Lübeck, 23560, Lübeck, Wallstraße 40, Germany

    Bernd Fischer

  2. Dipartimento di Matematica, Università degli Studi della Basilicata, c.da Macchia Romana, 85100, Potenza, Italy

    Woula Themistoclakis

Authors
  1. Bernd Fischer
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  2. Woula Themistoclakis
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Fischer, B., Themistoclakis, W. Orthogonal Polynomial Wavelets. Numerical Algorithms 30, 37–58 (2002). https://doi.org/10.1023/A:1015689418605

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