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Examples of frames on the Cantor dyadic group

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Abstract

We present two ways to construct frames on the locally compact Cantor dyadic group. The first approach gives a Parseval frame related to the generalized Walsh–Dirichlet kernel, while the second approach includes the Daubechies-type “admissible condition” and leads to dyadic compactly supported wavelet frames. The corresponding wavelet constructions on the Cantor and Vilenkin groups (as well as on the half-line \( {\mathbb{R}_{+} } \)) requires an additional constraint related to the requirement that the masks have no blocking sets.

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  1. Russian State Geological Prospecting University 23, Miklouho-Maklay Str., Moscow, 117997, Russia

    Yuri A. Farkov

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  1. Yuri A. Farkov
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Correspondence to Yuri A. Farkov.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 9, No. 2, pp. 175–190, April–May, 2012.

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Farkov, Y.A. Examples of frames on the Cantor dyadic group. J Math Sci 187, 22–34 (2012). https://doi.org/10.1007/s10958-012-1046-2

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