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unpublished results throughout the book.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.
Readership
Graduate students, research mathematicians, physicists,
and other scientists working in wavelet analysis.