LDR 03035 2200337 4500 010 _a9780821804759 _bbr. 011 _a0065-9266 090 _a12890 101 _aeng 102 _aUS 100 _a20120907 frey50 200 _aWavelet methods for pointwise regularity and local oscillations of functions _bM _fStéphane Jaffard, Yves Meyer 210 _aProvidence (R.I.) _cAmerican Mathematical Society _d1996 215 _a1 vol. (IX-110 p.) _d26 225 _9170211 _aMemoirs of the American Mathematical Society _v587 _x0065-9266 320 _aBibliogr. p. 106-108. Index 330 _aCurrently, 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) 410 _9170209 _aAMS _tMemoirs of the American Mathematical Society _v0587 _x0065-9266 676 _a2010 686 _20 _9164160 _a42C40 _bHarmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis _xWavelets and other special systems 686 _20 _9162810 _a26A16 _bReal functions -- Functions of one variable _xLipschitz (Hölder) classes 686 _20 _9162882 _a28A80 _bMeasure and integration -- Classical measure theory _xFractals 686 _20 _9162815 _a26A30 _bReal functions -- Functions of one variable _xSingular functions, Cantor functions, functions with other special properties 686 _20 _9164148 _a42B25 _bHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables _xMaximal functions, Littlewood-Paley theory 686 _20 _9164126 _a42A16 _bHarmonic analysis on Euclidean spaces -- Harmonic analysis in one variable _xFourier coefficients, Fourier series of functions with special properties, special Fourier series 700 _4070 _9174275 _aJaffard _bStéphane _f1962- 701 _4070 _9170838 _aMeyer _bYves _f1939- 905 _aec _b2012 906 _aec _b2012-09-07 995 _f08245-01 _xachat Dawson _917270 _cCMI _20 _kSéries AMS _o0 _eCouloir _z48.13 _bCMI 001 12890