Construction of Wavelets Through Walsh Functions, 1st ed. 2019 Industrial and Applied Mathematics Series

This book focuses on the fusion of wavelets and Walsh analysis, which involves non-trigonometric function series (or Walsh?Fourier series). The primary objective of the book is to systematically present the basic properties of non-trigonometric orthonormal systems such as the Haar system, Haar?Vilenkin system, Walsh system, wavelet system and frame system, as well as updated results on the book?s 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 and researchers interested in applied analysis.

Chapter 1. Introduction to Walsh Analysis and Wavelets

Chapter 2. Walsh-Fourier Series

Chapter 3. Haar–Fourier Analysis

Chapter 4. Construction of Dyadic Wavelets through Walsh Functions

Chapter 5. Orthogonal And Periodic Wavelets On Vilenkin Groups

Chapter 6. Haar-Vilenkin Wavelet

Chapter 7. Construction Biorthogonal Wavelets and Frames

Chapter 8. Wavelets associated with Nonuniform Multiresolution analysis on positive half line

Chapter 9. Orthogonal Vector Valued Wavelets on R+.

YURI A. FARKOV is a distinguished scientist and professor at the Russian Presidential Academy of National Economy and Public Administration (RANEPA), Moscow, Russia. Earlier, he worked as a professor and head of the Department of Mathematics at the Russian State Geological Prospecting University, Moscow, Russia, from 1997 to 2014; a professor and head of the Department of Higher  Mathematics at Dubna International University, Dubna, Russia, from 1996 to 2000; an associate professor at the Department of Higher Mathematics and Mathematical Modelling, Moscow State Geological Prospecting Academy, from 1988 to 1997; and a lecturer at the Department of Higher Mathematics, Moscow State University of Mechanical Engineering “Environmental and Chemical Engineering Institute”, Moscow, from 1981 to 1988. In 2013, Prof. Farkov received his DSc-Doctor Fiz.- Mat. Nauk from the People’s Friendship University of Russia on “Optimal Methods of Approximation of Function by Generalized Polynomials and Wavelets”. In 1981, he received his PhD degree in Mathematics from Moscow Region Pedagogical Institute, on topic “Investigations of Asymptotic and Approximation Properties of Faber–Erokhin Basis Functions”. From 1977 to 1980, he did his postgraduate studies at the Moscow Electro-Technical Engineering Institute; and in 1975, he received his BSc degree in Mathematics from Uralsk Pedagogical Institute, Kazakhstan. Professor Farkov is on the editorial boards of the journals American Journal of Computational Mathematics, Communications in Mathematics and Applications and International Journal of Education. He is a member of the Moscow Mathematical Society and American Mathematical Society. His research interests include mathematical analysis, wavelet theory, dyadic analysis and approximation theory. 

PAMMY MANCHANDA is a senior professor of mathematics at Guru Nanak Dev University, Amritsar, India. She has attended and delivered talks and c