A First Course on Wavelets

Bases for L2(R) Preliminaries Orthonormal Bases Generated by a Single Function: The Balian-Low Theorem Smooth Projections on L2(R) Local Sine and Cosine Bases and the Construction of Some Wavelets The Unitary Folding Operators and the Smooth Projections Notes and References Multiresolution Analysis and the Construction of Wavelets Multiresolution Analysis Construction of Wavelets from a Multiresolution Analysis The Construction of Compactly Supported Wavelets Better Estimates for the Smoothness of Compactly Supported Wavelets Notes and References Band-Limited Wavelets Orthonormality Completeness The Lemarie-Meyer Wavelets Revisited Characterization of Some Band-Limited Wavelets Notes and References Other Constructions of Wavelets Franklin Wavelets on the Real Line Spline Wavelets on the Real Line Orthonormal Bases of Piecewise Linear Continuous Functions for L2(T) Orthonormal Bases of Periodic Splines Periodization of Wavelets Defined on the Real Line Notes and References Representation of Functions by Wavelets Bases for Banach Spaces Unconditional Bases for Banach Spaces Convergence of Wavelet Expansions in LP(R) Pointwise Convergence of Wavelets Expansions H1 and BMO on R Wavelets as Unconditional Bases for H1(R) and LP(R) with 1