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Step wavelets on Vilenkin groups

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Abstract

The construction of wavelet bases and frames on the Vilenkin group Gp is studied. Wavelet systems consisting of functions that are compactly supported and band-limited at the same time are of our interest. A complete description of all refinable functions providing such systems is given.

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Funding

The second author was supported by the Russian Science Foundation (grant 18-11-00055); Definition 1 and Theorems 1–3 are due to this author.

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Authors and Affiliations

  1. Russian Presidential Academy of National Economy and Public Administration, Moscow, Russia

    Yu. Farkov

  2. Saint Petersburg State University, St. Petersburg, Russia

    M. Skopina

  3. Regional Mathematical Center of Southern Federal University, Rostov-on-Don, Russia

    M. Skopina

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  1. Yu. Farkov
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  2. M. Skopina
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Correspondence to M. Skopina.

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Farkov, Y., Skopina, M. Step wavelets on Vilenkin groups. J Math Sci 266, 696–708 (2022). https://doi.org/10.1007/s10958-022-06038-w

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