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Discrete wavelets and the Vilenkin-Chrestenson transform

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Abstract

In the spaces of complex periodic sequences, we use the Vilenkin-Chrestenson transforms to construct new orthogonal wavelet bases defined by finite collections of parameters. Earlier similar bases were defined for the Cantor and Vilenkin groups by means of generalized Walsh functions. It is noted that similar constructions can be realized for biorthogonal wavelets as well as for the space ℓ 2(ℤ+).

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Authors and Affiliations

  1. Russian State Geological Prospecting University, Moscow, Russia

    Yu. A. Farkov

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  1. Yu. A. Farkov
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Correspondence to Yu. A. Farkov.

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Original Russian Text © Yu. A. Farkov, 2011, published in Matematicheskie Zametki, 2011, Vol. 89, No. 6, pp. 914–928.

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Farkov, Y.A. Discrete wavelets and the Vilenkin-Chrestenson transform. Math Notes 89, 871–884 (2011). https://doi.org/10.1134/S0001434611050282

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