Mathematics > Classical Analysis and ODEs
[Submitted on 7 May 2024
]
Title: A characterization of wavelet sets on Vilenkin groups with its application to construction of MRA wavelets
Title: Vilenkin群上小波集的表征及其在MRA小波构造中的应用
Abstract: Let $G$ be a Vilenkin group. In 2008, Y. A. Farkov constructed wavelets on $G$ via the multiresolution analysis method. In this article, a characterization of wavelet sets on $G$ 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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