Orthogonal Wavelet Bases on Generalized Vilenkin Groups
M. Babushkin, M. Skopina
TL;DR
This paper develops an algorithmic approach to construct orthogonal wavelet bases with compact support on generalized Vilenkin groups, expanding wavelet theory in non-Archimedean settings.
Contribution
It introduces a novel method for constructing orthogonal wavelet bases on generalized Vilenkin groups, including explicit algorithms and compactly supported functions.
Findings
Constructed orthogonal wavelet bases on generalized Vilenkin groups
Provided an algorithm for wavelet basis construction
Wavelet bases have compactly supported Fourier transforms
Abstract
Wavelet systems on the generalized Vilenkin groups are considered. An algorithmic method for the construction of orthogonal wavelet bases is presented. These bases consist of compactly supported test functions (i.e. functions whose Fourier transform is also compactly supported).
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