LDR 03035     2200337   4500
010    _a9780821804759
011    _a0065-9266
090    _a12890
101    _aeng
102    _aUS
100    _a20120907              frey50       
200    _aWavelet methods for pointwise regularity and local oscillations of functions
       _fStéphane Jaffard, Yves Meyer
210    _aProvidence (R.I.)
       _cAmerican Mathematical Society
215    _a1 vol. (IX-110 p.)
225    _9170211
       _aMemoirs of the American Mathematical Society
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
       _tMemoirs of the American Mathematical Society
676    _a2010
686    _20
       _bHarmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis
       _xWavelets and other special systems
686    _20
       _bReal functions -- Functions of one variable
       _xLipschitz (Hölder) classes
686    _20
       _bMeasure and integration -- Classical measure theory
686    _20
       _bReal functions -- Functions of one variable
       _xSingular functions, Cantor functions, functions with other special properties
686    _20
       _bHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables
       _xMaximal functions, Littlewood-Paley theory
686    _20
       _bHarmonic analysis on Euclidean spaces -- Harmonic analysis in one variable
       _xFourier coefficients, Fourier series of functions with special properties, special Fourier series
700    _4070
701    _4070
905    _aec
906    _aec
995    _f08245-01
       _xachat Dawson
       _kSéries AMS
001     12890
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