Characterization of the pseudo-scaling functions on Vilenkin group

TL;DR

This paper characterizes pseudo-scaling functions and Parseval frame multiwavelets in Vilenkin groups, expanding the understanding of wavelet analysis on these mathematical structures.

Contribution

It introduces pseudo-scaling functions and generalized low pass filters in Vilenkin groups, providing new tools for wavelet analysis in this setting.

Findings

Characterization of Parseval frame multiwavelets in Vilenkin groups

Introduction of pseudo-scaling functions and their properties

Development of generalized low pass filters for Vilenkin groups

Abstract

Vilenkin groups, introduced by F. Ya Vilenkin, form a class of locally compact abelian groups. The present paper consists of the characterization of Parseval frame multiwavelets associated to multiresolution analysis (MRA) in the Vilenkin group. Further, we introduce the pseudo-scaling function along with a class of generalized low pass filters and study their properties in Vilenkin group.