DOI: 10.1515/gmj-2026-3021 ISSN: 1072-947X

Characterization of principal shift-invariant spaces on Vilenkin group

Prasadini Mahapatra, Ram Mohapatra
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Abstract

Translation generated spaces of square-integrable functions on the Vilenkin group are studied using a C-bracket. Principal shift-invariant spaces are characterized via the periodization function and the C-bracket. Conditions for semi-orthogonal Parseval wavelets are established, leading to a generalized multiresolution analysis (GMRA) of the semi-orthogonal Parseval frame. Examples are provided to support and illustrate the theoretical results.

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