Springer Construction of Wavelets Through Walsh Functions (Industrial and Applied Mathematics)

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. Review “The monograph is well written and the main concepts are clearly explained and presented. The contents are a comprehensive collection of results published during the last decades. The material is accessible to advanced undergraduate and graduate students with a good background in functional and Fourier analysis. For researchers, the volume is attractive for the broad and detailed presentation of the subject.” (Peter R. Massopust, Mathematical Reviews, November, 2019) “This book has an extensive bibliography of nearly 200 items and will be a valuable reference source. Since most chapters have exercises it could also be used as a textbook in an advanced graduate course. This work is noteworthy for its thoroughness, clarity, and historical perspective.” (Richard A. Zalik, zbMath 1418.42002, 2019) From the Back Cover 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. About the Author 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 Mathe