Overview
- Focuses on the fusion of wavelets and Walsh analysis, involving non-trigonometric function series
- Presents the basic properties of non-trigonometric orthonormal systems
- Discusses the most important results of Walsh and Haar analysis
- Identifies the Haar wavelet as the simplest example of a wavelet, and the Walsh function as the first example of a wavelet packet
Part of the book series: Industrial and Applied Mathematics (INAMA)
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Table of contents (9 chapters)
Keywords
About this book
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.
Reviews
“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)
Authors and Affiliations
About the authors
PAMMY MANCHANDA is a senior professor of mathematics at Guru Nanak Dev University, Amritsar, India. She has attended and delivered talks and chaired sessions at reputed academic conferences and workshops across the world, including ICIAM (1999–2015) and ICM since 2002. She was invited twice to the Industrial Mathematics Group of Professor Helmut Neunzert, Kaiserslautern University, Germany, and visited the International Centre for Theoretical Physics (a UNESCO institution) at Trieste, Italy, many times to carry out her research activities. She was the joint secretary of the Indian Society of Industrial and Applied Mathematics (ISIAM) from 1999 until 2016 and after that, she is the secretary of the society. She has been actively engaged in organizing international conferences by the society. She is the managing editor of the Indian Journal of Industrial and Applied Mathematics (by ISIAM) and a member of the editorial board of the Springer’s book series, Industrial and Applied Mathematics. With a research interest in functional analysis and applications (financial and meteorological data) and wavelet theory, Prof.Manchanda has published 54 research papers in several international journals of repute, edited 3 proceedings of international conferences of ISIAM and co-authored 3 books.
ABUL HASAN SIDDIQI is a distinguished scientist and professor emeritus at the School of Basic Sciences and Research at Sharda University, Greater Noida, India. He was also a visiting consultant at the International Centre for Theoretical Physics (ICTP), Trieste, Italy; Sultan Qaboos University, Muscat, Oman; MIMOS, Kuala Lumpur, Malaysia; and professor at several reputed universities including Aligarh Muslim University (Aligarh, India) and King Fahd University of Petroleum & Minerals (Dhahran, Saudi Arabia). He has a long association with ICTP (a UNESCO institution) in several capacities: short-time visitor, long-duration visitor, regular associate, guests of the director and senior associate. He was awarded the German Academic Exchange Fellowship thrice to carry out mathematical research in Germany. He has published more than 100 research papers jointly with his research collaborators, 5 books and edited proceedings of 9 international conferences, as well as supervised 29 PhD scholars. He is the founder secretary and the elected president of the Indian Society of Industrial and Applied Mathematics (ISIAM), which celebrated its silver jubilee year in January 2016. He is the editor-in-chief of Indian Journal of Industrial and Applied Mathematics (published by ISIAM) and the Springer’s book series, Industrial and Applied Mathematics.
Bibliographic Information
Book Title: Construction of Wavelets Through Walsh Functions
Authors: Yu. A. Farkov, Pammy Manchanda, Abul Hasan Siddiqi
Series Title: Industrial and Applied Mathematics
DOI: https://doi.org/10.1007/978-981-13-6370-2
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. 2019
Hardcover ISBN: 978-981-13-6369-6Published: 14 May 2019
Softcover ISBN: 978-981-13-6372-6Published: 14 August 2020
eBook ISBN: 978-981-13-6370-2Published: 29 April 2019
Series ISSN: 2364-6837
Series E-ISSN: 2364-6845
Edition Number: 1
Number of Pages: XXII, 381
Topics: Analysis