Wavelet methods for pointwise regularity and local oscillations of functions / Stéphane Jaffard, Yves Meyer

Auteur: Jaffard, Stéphane (1962-) - AuteurCo-auteur: Meyer, Yves (1939-) - AuteurType de document: MonographieCollection: Memoirs of the American Mathematical Society ; 587Langue: anglaisPays: Etats UnisÉditeur: Providence (R.I.) : American Mathematical Society, 1996Description: 1 vol. (IX-110 p.) ; 26 cm ISBN: 9780821804759 ; br. ISSN: 0065-9266Résumé: Currently, new trends in mathematics are emerging from the fruitful interaction between signal processing, image processing, and classical analysis. One example is given by "wavelets", which incorporate both the know-how of the Calderon-Zygmund school and the efficiency of some fast algorithms developed in signal processing (quadrature mirror filters and pyramidal algorithms.) A second example is "multi-fractal analysis". The initial motivation was the study of fully developed turbulence and the introduction by Frisch and Parisi of the multi-fractal spectrum. Multi-fractal analysis provides a deeper insight into many classical functions in mathematics. A third example--"chirps"--is studied in this book. Chirps are used in modern radar or sonar technology. Once given a precise mathematical definition, chirps constitute a powerful tool in classical analysis. In this book, wavelet analysis is related to the 2-microlocal spaces discovered by J. M. Bony. The authors then prove that a wavelet based multi-fractal analysis leads to a remarkable improvement of Sobolev embedding theorem. In addition, they show that chirps were hidden in a celebrated Riemann series. (Source : AMS).Bibliographie: Bibliogr. p. 106-108. Index. Sujets MSC: 42C40 Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- Wavelets and other special systems
26A16 Real functions -- Functions of one variable -- Lipschitz (Hölder) classes
28A80 Measure and integration -- Classical measure theory -- Fractals
26A30 Real functions -- Functions of one variable -- Singular functions, Cantor functions, functions with other special properties
42B25 Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Maximal functions, Littlewood-Paley theory
42A16 Harmonic analysis on Euclidean spaces -- Harmonic analysis in one variable -- Fourier coefficients, Fourier series of functions with special properties, special Fourier series
Location Call Number Status Date Due
Couloir 08245-01 / Séries AMS (Browse Shelf) Available

Bibliogr. p. 106-108. Index

Currently, new trends in mathematics are emerging from the fruitful interaction between signal processing, image processing, and classical analysis.

One example is given by "wavelets", which incorporate both the know-how of the Calderon-Zygmund school and the efficiency of some fast algorithms developed in signal processing (quadrature mirror filters and pyramidal algorithms.)

A second example is "multi-fractal analysis". The initial motivation was the study of fully developed turbulence and the introduction by Frisch and Parisi of the multi-fractal spectrum. Multi-fractal analysis provides a deeper insight into many classical functions in mathematics.

A third example--"chirps"--is studied in this book. Chirps are used in modern radar or sonar technology. Once given a precise mathematical definition, chirps constitute a powerful tool in classical analysis.

In this book, wavelet analysis is related to the 2-microlocal spaces discovered by J. M. Bony. The authors then prove that a wavelet based multi-fractal analysis leads to a remarkable improvement of Sobolev embedding theorem. In addition, they show that chirps were hidden in a celebrated Riemann series. (Source : AMS)

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