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 be a Vilenkin group. In 2008, Y. A. Farkov constructed wavelets on via the multiresolution analysis method. In this article, a characterization of wavelet sets on 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].
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}
}
Comments
28 pages