• Presents tutorial-style discussions by leading mathematicians on the subject of wavelets and related topics such as neural networks and potential theory
• Presents pioneering work in the area of the approximation properties of neural networks
• Illustrates applications of classical wavelet theory in quantum mechanics
• Elaborates upon polynomial and trigonometic polynomial wavelets and frames
• Explores the quantitative description of the asymptotic distribution of zeros of orthogonal and other polynomials and extends these ideas in the multi-dimensional setting.

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