Construction of wavelets through Walsh functions
著者
書誌事項
Construction of wavelets through Walsh functions
（Industrial and applied mathematics）
Springer, c2019
- : [pbk.]
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
Chapter 1. Introduction to Walsh Analysis and WaveletsChapter 2. Walsh-Fourier SeriesChapter 3. Haar-Fourier AnalysisChapter 4. Construction of Dyadic Wavelets through Walsh FunctionsChapter 5. Orthogonal And Periodic Wavelets On Vilenkin GroupsChapter 6. Haar-Vilenkin WaveletChapter 7. Construction Biorthogonal Wavelets and FramesChapter 8. Wavelets associated with Nonuniform Multiresolution analysis on positive half lineChapter 9. Orthogonal Vector Valued Wavelets on R+.
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