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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 behaviour 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 A pioneer of the wavelet ""saga"", Meyer gives new and as yet unpublished results throughout the book.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." Full Product DetailsAuthor: Yves MeyerPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: No. 9 Dimensions: Width: 18.40cm , Height: 1.30cm , Length: 26.70cm Weight: 0.480kg ISBN: 9780821806852ISBN 10: 0821806858 Pages: 133 Publication Date: 30 November 1997 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsIntroduction Scaling exponents at small scales Infrared divergences and Hadamard's finite parts The 2-microlocal spaces C^{s,s^{\prime}}_{x_0}$ New characterizations of the two-microlocal spaces An adapted wavelet basis Combining a Wilson basis with a wavelet basis Bibliography Index Greek symbols Roman symbols.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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