Wavelet Sets and Generalized Scaling Sets on Vilenkin Group

TL;DR

This paper demonstrates the construction of single wavelets on Vilenkin groups using wavelet sets, extending beyond MRA-based methods, and explores properties of generalized scaling sets.

Contribution

It introduces a new approach to construct single wavelets on Vilenkin groups via wavelet sets, not relying on MRA, and characterizes their properties and relationships with generalized scaling sets.

Findings

Constructed single wavelets on Vilenkin groups using wavelet sets.

Characterized single and multi-wavelet sets on Vilenkin groups.

Explored properties and relations of generalized scaling sets.

Abstract

For Vilenkin group only the existence of multiwavelets associated with multiresolution analysis (MRA) is known. In this paper, we have shown that by using wavelet sets we can also construct single wavelet in case of Vilenkin group which are not associated with MRA.We have given characterization of single and multi-wavelet sets on Vilenkin group. Further, we have studied generalized scaling sets, some of their properties and relation between wavelet sets and generalized scaling sets.