# Wavelet sets on Cantor Dyadic Group

## TL;DR

This paper characterizes wavelet sets on the Cantor dyadic group, offering a new construction method that does not always rely on multiresolution analysis, and explores their relation with existing wavelet frameworks.

## Contribution

It provides a novel characterization of wavelet sets on the Cantor dyadic group and establishes their connection with multiresolution analysis, including relevant examples.

## Key findings

- New characterization method for wavelet sets on Cantor dyadic group
- Not all wavelets from wavelet sets are linked to multiresolution analysis
- Examples illustrating the relationship between wavelet sets and MRA

## Abstract

W. C. Lang determined wavelets on Cantor dyadic group by using Multiresolution analysis method. In this paper we have given characterization of wavelet sets on Cantor dyadic group providing another method for the construction of wavelets. All the wavelets originating from wavelet sets are not necessarily associated with a multiresolution analysis. Relation between multiresolution analysis and, wavelets determined from wavelet sets is established along with relevant examples.

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Source: https://tomesphere.com/paper/1906.07700