About this Title
I. Ya. Novikov, Voronezh State University, Voronezh, Russia, V. Yu. Protasov, Moscow State University, Moscow, Russia and M. A. Skopina, St. Petersburg University, St. Petersburg, Russia. Translated by Evgenia Sorokina
Publication: Translations of Mathematical Monographs
Publication Year: 2011; Volume 239
ISBNs: 978-0-8218-4984-2 (print); 978-1-4704-1625-6 (online)
MathSciNet review: MR2779330
MSC: Primary 42-02; Secondary 41A60, 42C15, 42C40, 46E30
Wavelet theory lies on the crossroad of pure and computational mathematics, with connections to audio and video signal processing, data compression, and information transmission.
The present book is devoted to a systematic exposition of modern wavelet theory. It details the construction of orthogonal and biorthogonal systems of wavelets and studies their structural and approximation properties, starting with basic theory and ending with special topics and problems. The book also presents some applications of wavelets. Historical commentary is supplied for each chapter in the book, and most chapters contain exercises.
The book is intended for professional mathematicians and graduate students working in functional analysis and approximation theory. It is also useful for engineers applying wavelet theory in their work. Prerequisites for reading the book consist of graduate courses in real and functional analysis.
Graduate students and research mathematicians interested in wavelet theory.
Table of Contents
- Wavelets on the line
- Multivariate wavelets
- Compactly supported refinable functions
- Wavelets with compact support
- Fractal properties of wavelets
- Factorization of refinement equations
- Smoothness of compactly supported wavelets
- Nonstationary wavelets
- Periodic wavelets
- Approximation by periodic wavelets
- Remarkable properties of wavelet bases
- Auxiliary facts of the theory of functions and functional analysis
- Historical comments