Wavelet sets, scaling sets and generalized scaling sets on Vilenkin group

Abstract

Wavelet sets provide a range of wavelets that can be analyzed with ease. The constructions of wavelet sets and scaling sets in different settings are studied in several papers in the literature. Wavelet sets provide a good source of examples and counterexamples in wavelet theory. In this paper we have studied properties of (multi)wavelet sets and associated wavelets for Vilenkin group. Further, results related to scaling sets and generalized scaling sets are given along with some characterizations.