The study of wavelets has grown tremendously over the past decade and found myriad applications in areas such as image processing, signal processing, data compression, and numerical methods. This volume contains articles by eminent mathematicians on aspects of wavelet theory. These chapters include a systematic study of the approximation properties of neural networks and a look at several applications where classical approaches were found to be inadequate, such as the numerical solution of sparse matrix equations and the construction of wavelets using spline functions, but supported only on a compact interval and
Table of Contents
Continuous Wavelet Transform: An Introduction. Introducing Wavelets Through Splines and Multiresolution Analysis. Compactly Supported Wavelets. Abelian Theorems for the Wavelet Transform. Wavelets as Unconditional Bases for the Spaces L^P(R), 1 less than p less than alpha-S. Wavelets and Unconditional Bases in Approximation Theory. Introduction to Frames. Random Schrodinger Operators with Wavelet Interactions. Spline Wavelets on an Interval. Trigonometric Wavelets. From Orthogonal Polynomials to iteration Schemes for Linear Systems: CG and CR Revisited. Approximation Theory and Neural Networks. Orthogonal Polynomials, Potential Theory and discrepancy Theorems. Potential Theory and Discrepancy Estimates in Higher Dimensions.