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A characterization of wavelet sets on Vilenkin groups with its application to construction of MRA wavelets

Classical Analysis and ODEs 2024-05-08 v1 Analysis of PDEs Functional Analysis

Abstract

Let GG be a Vilenkin group. In 2008, Y. A. Farkov constructed wavelets on GG via the multiresolution analysis method. In this article, a characterization of wavelet sets on GG is established, which provides another method for the construction of wavelets. As an application, the relation between multiresolution analyses and wavelets determined from wavelet sets is also presented. To some extent, these results positively answer a question mentioned by P. Mahapatra and D. Singh in [Bull. Sci. Math. 167 (2021), Paper No. 102945, 20 pp].

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Cite

@article{arxiv.2405.04220,
  title  = {A characterization of wavelet sets on Vilenkin groups with its application to construction of MRA wavelets},
  author = {Jun Liu and Chi Zhang},
  journal= {arXiv preprint arXiv:2405.04220},
  year   = {2024}
}

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28 pages