Wavelets Mathematics and Applications

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

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 MaterialConstruction of Orthonormal Wavelets, R.S. StrichartzAn Introduction to the Orthonormal Wavelet Transform on Discrete Sets, M. Frazier and A. KumarGabor Frames for L2 and Related Spaces, J.J. Benedetto and D.F. WalnutDilation Equations and the Smoothness of Compactly Supported Wavelets, C. Heil and D. ColellaRemarks on the Local Fourier Bases, P. AuscherWavelets and Signal ProcessingThe Sampling Theorem, Phi-Transform, and Shannon Wavelets for R, Z, T, and ZN, M. Frazier and R. TorresFrame Decompositions, Sampling, and Uncertainty Principle Inequalities, J.J. BenedettoTheory and Practice of Irregular Sampling, H.G. Feichtinger and K. GröchenigWavelets, Probability, and Statistics: Some Bridges, C. HoudréWavelets and Adapted Waveform Analysis, R.R. Coifman and V. WickerhauserNear Optimal Compression of Orthonormal Wavelet Expansions, B. Jawerth, C.-C. Hsiao, B. Lucier, and X. YuWavelets and Partial Differential OperatorsOn Wavelet-Based Algorithms for Solving Differential Equations, G. BeylkinWavelets and Nonlinear Analysis, S. JaffardScale Decomposition in Burgers' Equation, F. Heurtaux, F. Planchon, and V. WickerhauserThe Cauchy Singular Integral Operator and Clifford Wavelets, L. Andersson, B. Jawerth, and M. MitreaThe Use of Decomposition Theorems in the Study of Operators, R. Rochberg