Wavelets Mathematics and Applications [Hardcover]

Wavelets is a carefully organized and edited collection of extended survey papers addressing key topics in the mathematical foundations and applications of wavelet theory. The first part of the book is devoted to the fundamentals of wavelet analysis. The construction of wavelet bases and the fast computation of the wavelet transform in both continuous and discrete settings is covered. The theory of frames, dilation equations, and local Fourier bases are also presented.

The second part of the book discusses applications in signal analysis, while the third part covers operator analysis and partial differential equations. Each chapter in these sections provides an up-to-date introduction to such topics as sampling theory, probability and statistics, compression, numerical analysis, turbulence, operator theory, and harmonic analysis.
The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. It will be an especially useful reference for harmonic analysts, partial differential equation researchers, signal processing engineers, numerical analysts, fluids researchers, and applied mathematicians.Core Material
Construction of Orthonormal Wavelets, R.S. Strichartz
An Introduction to the Orthonormal Wavelet Transform on Discrete Sets, M. Frazier and A. Kumar
Gabor Frames for L2 and Related Spaces, J.J. Benedetto and D.F. Walnut
Dilation Equations and the Smoothness of Compactly Supported Wavelets, C. Heil and D. Colella
Remarks on the Local Fourier Bases, P. Auscher
Wavelets and Signal Processing
The Sampling Theorem, Phi-Transform, and Shannon Wavelets for R, Z, T, and ZN, M. Frazier and R. Torres
Frame Decompositions, Sampling, and Uncertainty Principle Inequalities, J.J. Benedetto
Theory and Practice of Irregular Sampling, H.G. Feichtinger and K. Gr?chenig
Wavelets, Probability, and Statistics: Some Bridges, C. Houdr?
Wavelets and Adapted Waveforló-