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28A80 Measure and integration -- Classical measure theory -- Fractals

42B05 Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Fourier series and coefficients

46Nxx Functional analysis -- Miscellaneous applications of functional analysis

60G18 Probability theory and stochastic processes -- Stochastic processes -- Self-similar processes En-ligne: Springerlink | zbMath | MSN

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This is an unusual book in analysis, since it covers subjects not often found in analysis books: wavelets, fractals and signals. But, as the author puts it, “the ideas involved in this book are intuitive, natural, many of them visual, and geometric”. Also, “despite the inclusion of themes from probability and even from engineering, the course still has an underlying core theme: A constructive approach to building bases in function spaces”. “Constructive” means the use of recursive algorithms.

The content of the book varies from measures on path spaces, random walks, duality for Cantor sets, infinite products, the minimal eigenfunction to wavelets, pyramid algorithms and operators and multiresolution analysis.

Separate sections in the book explain engineering terms to mathematicians, and operator theory to engineers.

Each chapter concludes with a helpful guide to the literature allowing students to follow up on topics in the book.

The book should be useful for a second course in analysis, especially for students in engineering, physics and statistics. (zbMath)

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