Wavelets and Other Orthogonal Systems (Hardcover, 2)

ORTHOGONAL SERIES
General Theory
Examples
A PRIMER ON TEMPERED DISTRIBUTIONS
Intuitive Introduction
Test Functions
Tempered Distribution
Fourier Transforms
Periodic Distributions
Analytic Representations
Sobolev Spaces
AN INTRODUCTION TO ORTHOGONAL WAVELET THEORY
Multiresolution Analysis
Mother Wavelet
Reproducing Kernels and a Moment Condition
Regularity of Wavelets as a Moment Condition
Mallat's Decomposition and Reconstruction Algorithm
Filters
CONVERGENCE AND SUMMABILITY OF FOURIER SERIES
Pointwise Convergence
Summability
Gibbs' Phenomenon
Periodic Distributions
WAVELETS AND TEMPERED DISTRIBUTIONS
Multiresolution Analysis of Tempered Distributions
Wavelets Based on Distributions
Distributions with Point Support
Approximation with Impulse Trains
ORTHOGONAL POLYNOMIALS
General Theory
Classical Orthogonal Polynomials
Problems
OTHER ORTHOGONAL SYSTEMS
Self-Adjoint Eigenvalue Problems on Finite Intervals
Hilber-Schmnidt Integral Operators
An Anomaly: The Prolate Spheroidal Functions
A Lucky Accident?
Rademacher Functions
Walsh Function
Periodic Wavelets
Local Sine or Cosine Base
Biorthogonal Wavelets
POINTWISE CONVERGENCE OF WAVELET EXPANSIONS
Reproducing Kernel Delta Sequences
Positive and Quasi-Positive Delta Sequences
Local Convergence of Distribution Expansions
Convergence Almost Everywhere
Rate of Convergence of the Delta Sequence
Other Partial Sums of the Wavelet Expansion
Gibbs' Phenomenon
Positive Scaling Functions
A SHANNON SAMPLING THEOREM IN WAVELET SUBSPACES
A Riesz Basis of Vm
The Ampling Sequence in Vm
Examples of Sampling theorems
The Sampling Sequence in Tm
Shifted Sampling
Gibbs' Phenomenon for Sampling Series
Irregular Sampling in Wavelet Subspaces
EXTENSIONS OF WAVELET SAMPLING THEOREMS
Oversampling with Scaling Functions
Hybrid Sampling Series
Positive Hybrid Sampling
The Convergence of the Positive Hybrid Series
Cardinal Scaling Functions
Interpolating Multiwavelets
Orthogonal Finite Element Multiwavelets
TRANSLATION AND DILATION INVARIANCE IN ORTHOGONAL SYSTEMS
Trigonometric System
Orthogonal Polynomials
An Example Where Everything Works
An Example Where Nothing Works
Weak Translation Invariance
Dilations and Other Operations
ANALYTIC REPRESENTATIONS VIA ORTHOGONAL SERIES
Trigonometric Series
Hermite Series
Legendre Polynomial Series
Analytic and Harmonic Wavelets
Analytic Solutions to Dilation Equations
Analytic Representation of Distributions by Wavelets
Wavelets Analytic in the Entire Complex Plane
ORTHOGONAL SERIES IN STATISTICS
Fourier Series Density Estimators
Hermite Series Density Estimators
The Histogram as a Wavelet Estimator
Smooth Wavelet Estimators of Density
Local Convergence
Positive Density Estimators Based on Characteristic Functions
Positive Estimators Based on Positive Wavelets
Density Estimation with Noisy Data
Other Estimation with Wavelets
Threshold Methods
ORTHOGONAL SYSTEMS AND STOCHASTIC PROCESSES
K-L Expansions
Stationary Processes and Wavelets
A Series with Uncorrelated Coefficients
Wavelets Based on Band Limited Processes
Nonstationary Processes

Each chapter also contains a Problems section