Construction of Wavelets Through Walsh Functions

This book focuses on the fusion of wavelets and Walsh analysis, which involves non-trigonometric function series (or WalshFourier series). The primary objective of the book is to systematically present the basic properties of non-trigonometric orthonormal systems such as the Haar system, HaarVilenkin system, Walsh system, wavelet system and frame system, as well as updated results on the books main theme. Based on lectures that the authors presented at several international conferences, the notions and concepts introduced in this interdisciplinary book can be applied to any situation where wavelets and their variants are used. Most of the applications of wavelet analysis and Walsh analysis can be tried for newly constructed wavelets. Given its breadth of coverage, the book offers a valuable resource for theoreticians and those applying mathematics in diverse areas. It is especially intended for graduate students of mathematics and engineering andresearchers interested in applied analysis.