Wavelet Theory and Harmonic Analysis in Applied Sciences

The idea of this book originated in the works presented at the First Latinamerican Conference on Mathematics in Industry and Medicine, held in Buenos Aires, Argentina, from November 27 to December 1, 1995. A variety of topics were discussed at this meeting. A large percentage of the papers focused on Wavelet and Harmonic Analysis. The theory and applications of this topic shown at the Conference were interesting enough to be published. Based on that we selected some works which make the core of this book. Other papers are contributions written by invited experts in the field to complete the presentation. All the works were written after the Conference. The purpose of this book is to present recent results as well as theo retical applied aspects of the subject. We have decided not to include a section devoted to the theoretical foundations of wavelet methods for non specialists. There are excellent introductions already available, for example, Chapter one in Wavelets in Medicine and Biology, edited by A. Aldroubi and M. Unser, 1996, or some of the references cited in the chapter.

Inhalt
I Theory and Implementations.- 1 Singular integrals related to the Monge-Ampère equation.- 2 Wavelet characterization of functions with conditions on the mean oscillation.- 3 Undecimated Wavelet Transform from Orthogonal Spline Wavelets.- 4 Oblique Multiwavelet Bases.- 5 Frames and Riesz bases: a short survey.- 6 Fourier Analysis of Petrov-Galerkin Methods Based on Biorthogonal Multiresolution Analyses.- II Applications to Biomedical Sciences.- 7 Fine Structure of ECG Signal using Wavelet Transform.- 8 Spectral Analysis of Cardiorespiratory Signals.- 9 Characterization of Epileptic EEG Time Series (I): Gabor Transform and Nonlinear Dynamics Methods.- 10 Characterization of Epileptic EEG Time Series (II): Wavelet Transform and Information Theory.- III Applications in Physical Sciences.- 11 Wavelet Networks for Modelling Nonlinear Processes.- 12 Higher order asymptotic boundary conditions for an oxide region in a semiconductor device.- 13 Estimation of the complex plain-wave modulus in viscoelastic media.- 14 Numerical Modelling of Maxwell's Equations with Applications to Magnetotellurics.