Les ondelettes en 1989 : séminaire d'analyse harmonique, Université de Paris-sud, Orsay / P. G. Lemarié
Type de document : Livre numériqueCollection : Lecture notes in mathematics, 1438Langue : français.Éditeur : Berlin : Springer-Verlag, 1990ISBN: 9783540529323.ISSN: 1617-9692.Sujet MSC : 46B15, Functional analysis - Normed linear spaces and Banach spaces; Banach lattices, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces42Cxx, Harmonic analysis on Euclidean spaces - Nontrigonometric harmonic analysis
42C15, Nontrigonometric harmonic analysis, General harmonic expansions, frames
42-06, Proceedings, conferences, collections, etc. pertaining to harmonic analysis on Euclidean spacesEn-ligne : Springerlink | MathSciNet
... This text is a collection of nine expository lectures on wavelet theory. The first three lectures provide the motivation and the underlying ideas of wavelet theory and ample historical background.
The second third of the book is devoted to applications of wavelets to operator theory (a new and conceptually simple proof of the celebrated T(b)-theorem for Calderón-Zygmund operators), computer vision, and signal analysis.
The last part presents different facets of wavelets and fractals: iterative interpolation, the study of the local regularity of a function through the wavelet transform and a thorough investigation of Riemann's nondifferentiable function, and a wavelet approach to renormalization, turbulence and chaos.
The appendix contains detailed English summaries of each lecture, written by Lemarié. (MathSciNet)
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