Wavelets, Vibrations and Scalings

Wavelets, Vibrations and Scalings

by Yves Meyer
     
 

Physicists and mathematicians are intensely studying fractal sets of fractal curves. Mandelbrot advocated modeling of real-life signals by fractal or multifractal functions. One example is fractional Brownian motion, where large-scale behavior is related to a corresponding infrared divergence. Self-similarities and scaling laws play a key role in this new area.

See more details below

Overview

Physicists and mathematicians are intensely studying fractal sets of fractal curves. Mandelbrot advocated modeling of real-life signals by fractal or multifractal functions. One example is fractional Brownian motion, where large-scale behavior is related to a corresponding infrared divergence. Self-similarities and scaling laws play a key role in this new area. There is a widely accepted belief that wavelet analysis should provide the best available tool to unveil such scaling laws. And orthonormal wavelet bases are the only existing bases which are structurally invariant through dyadic dilations. This book discusses the relevance of wavelet analysis to problems in which self-similarities are important. Among the conclusions drawn are the following: 1) A weak form of self-similarity can be given a simple characterization through size estimates on wavelet coefficients, and 2) Wavelet bases can be tuned in order to provide a sharper characterization of this self-similarity. A pioneer of the wavelet ''saga'', Meyer gives new and as yet unpublished results throughout the book. It is recommended to scientists wishing to apply wavelet analysis to multifractal signal processing.

Read More

Product Details

ISBN-13:
9780821806852
Publisher:
American Mathematical Society
Publication date:
11/18/1997
Series:
Crm Monograph Series, #9
Pages:
133
Product dimensions:
7.09(w) x 10.63(h) x (d)

Meet the Author

Table of Contents

List of Figures
Preface
Introduction1
Ch. 1Scaling exponents at small scales5
Ch. 2Infrared divergences and Hadamard's finite parts43
Ch. 3The 2-microlocal spaces [actual symbol not reproducible]57
Ch. 4New characteristics of the two-microlocal spaces79
Ch. 5An adapted wavelet basis89
Ch. 6Combining a Wilson basis with a wavelet basis111
Bibliography127
Index129
Greek Symbols131
Roman Symbols133

Read More

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >