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Wavelets, Vibrations and Scalings (Crm Monograph Series)

Yves Meyer

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ISBN 10: 0821806858 / ISBN 13: 9780821806852
Published by American Mathematical Society, Centre de Recherches Mathematiques, 1997
New Condition: New Hardcover
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Title: Wavelets, Vibrations and Scalings (Crm ...

Publisher: American Mathematical Society, Centre de Recherches Mathematiques

Publication Date: 1997

Binding: Hardcover

Book Condition:New

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Synopsis:

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 A pioneer of the wavelet ``saga'', Meyer gives new and as yet unpublished results throughout the book.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.

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