Book contents
- Frontmatter
- Preface
- Contents
- Introduction
- I Preliminaries
- II Normed Linear Spaces
- III Hilbert Space
- IV Linear Operators
- V Linear Functionals
- VI Space of Bounded Linear Functionals
- VII Closed Graph Theorem and Its Consequences
- VIII Compact Operators on Normed Linear Spaces
- IX Elements of Spectral Theory of Self-Adjoint Operators in Hilbert Spaces
- X Measure and Integration in Lp Spaces
- XI Unbounded Linear Operators
- XII The Hahn-Banach Theorem and Optimization Problems
- XIII Variational Problems
- XIV The Wavelet Analysis
- XV Dynamical Systems
- List of Symbols
- Bibliography
- Index
XIV - The Wavelet Analysis
Published online by Cambridge University Press: 05 May 2013
- Frontmatter
- Preface
- Contents
- Introduction
- I Preliminaries
- II Normed Linear Spaces
- III Hilbert Space
- IV Linear Operators
- V Linear Functionals
- VI Space of Bounded Linear Functionals
- VII Closed Graph Theorem and Its Consequences
- VIII Compact Operators on Normed Linear Spaces
- IX Elements of Spectral Theory of Self-Adjoint Operators in Hilbert Spaces
- X Measure and Integration in Lp Spaces
- XI Unbounded Linear Operators
- XII The Hahn-Banach Theorem and Optimization Problems
- XIII Variational Problems
- XIV The Wavelet Analysis
- XV Dynamical Systems
- List of Symbols
- Bibliography
- Index
Summary
An Introduction to Wavelet Analysis
The concept of Wavelet was first introduced around 1980. It came out as a synthesis of ideas borrowed from disciplines including mathematics (Calderáon Zygmund operators and Littlewood-Paley theory), physics (coherent states formalism in quantum mechanism and renormalizing group) and engineering (quadratic mirror filters, sidebend coding in signal processing and pyramidal algorithms in image processing) (Debnath [17]).
Wavelet analysis provides a systematic new way to represent and analyze multiscale structures. The special feature of Wavelet analysis is to generalize and expand the representations of functions by orthogonal basis to infinite domains. For this purpose, compactly supported [see 13.5] basis functions are used and this linear combination represents the function. These are the kinds of functions that are realized by physical devices.
- Type
- Chapter
- Information
- A First Course in Functional AnalysisTheory and Applications, pp. 430 - 442Publisher: Anthem PressPrint publication year: 2013