Wavelet Theory and Harmonic Analysis in Applied Sciences

1. Front Matter

   Pages i-xviii

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2. Theory and Implementations

   1. Front Matter

      Pages 1-1

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   2. Singular integrals related to the Monge-Ampère equation

      • Luis A. Caffarelli, Cristian E. Gutiérrez

      Pages 3-13

   3. Wavelet characterization of functions with conditions on the mean oscillation

      • Hugo Aimar, Ana Bernardis

      Pages 15-32

   4. Undecimated Wavelet Transform from Orthogonal Spline Wavelets

      • Eduardo P. Serrano, Marcela A. Fabio

      Pages 33-72

   5. Oblique Multiwavelet Bases

      • Akram Aldroubi

      Pages 73-91

   6. Frames and Riesz bases: a short survey

      • S. J. Favier, R. A. Zalik

      Pages 93-117

   7. Fourier Analysis of Petrov-Galerkin Methods Based on Biorthogonal Multiresolution Analyses

      • Sônia M. Gomes, Elsa Cortina

      Pages 119-140

3. Applications to Biomedical Sciences

   1. Front Matter

      Pages 141-141

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   2. Fine Structure of ECG Signal using Wavelet Transform

      • Hervé Rix, Olivier Meste

      Pages 143-153

   3. Spectral Analysis of Cardiorespiratory Signals

      • Marcelo R. Risk, Jamil F. Sobh, Ricardo L. Armentano, Agustín J. Ramírez, J. Philip Saul

      Pages 155-177

   4. Characterization of Epileptic EEG Time Series (I): Gabor Transform and Nonlinear Dynamics Methods

      • Susana Blanco, Silvia Kochen, Rodrigo Quian Quiroga, Luis Riquelme, Osvaldo A. Rosso, Pablo Salgado

      Pages 179-226

   5. Characterization of Epileptic EEG Time Series (II): Wavelet Transform and Information Theory

      • Carlos E. D’Attellis, Lucas G. Gamero, Susana I. Isaacson, Ricardo O. Sirne, María E. Torres

      Pages 227-262

4. Applications in Physical Sciences

   1. Front Matter

      Pages 263-263

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   2. Wavelet Networks for Modelling Nonlinear Processes

      • N. Roqueiro, E. L. Lima

      Pages 265-299

   3. Higher order asymptotic boundary conditions for an oxide region in a semiconductor device

      • Irene M. Gamba

      Pages 301-314

   4. Estimation of the complex plain—wave modulus in viscoelastic media

      • E. M. Fernández-Berdaguer, J. E. Santos

      Pages 315-327

   5. Numerical Modelling of Maxwell’s Equations with Applications to Magnetotellurics

      • Luis Guarracino, Juan Enrique Santos

      Pages 329-345

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.

• Analysis
• Frames
• Gabor transform
• Singular integral
• Volume
• electrocardiogram (ECG)
• equation
• fourier analysis
• harmonic analysis
• information theory
• interaction
• modeling
• modelling
• wavelet
• wavelet transform

• Department of Mathematics, University of Buenos Aires, Buenos Aires, Argentina

  C. E. D’Attellis

• Instituto de Cálculo, Ciudad Universitaria — Pabellón II, Buenos Aires, Argentina

  E. M. Fernández-Berdaguer

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