Les Ondelettes en 1989: Séminaire d'Analyse Harmonique, by Pierre G. Lemarie

By Pierre G. Lemarie

This publication surveys the new concept of wavelet transforms and its purposes in quite a few fields either inside arithmetic (singular integrals, localization of singularities) and past it, in computing device imaginative and prescient, the physics of fractals, time-frequency research.

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Additional resources for Les Ondelettes en 1989: Séminaire d'Analyse Harmonique, Univ. de Paris-Sud, Orsay

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J o n e s & S. S e m m e s Two elementary proofs of the L 2 - b o u n d edness of Cauchy integrals on Lipschitz curves. J. Amer. Math. Soc. 2 (1989), 553-564. ID] G. D a v i d Noyau de Cauchy et op6rateurs de Calder6n-Zygmund. Thbse d'Etat, Paris X/, Centre Scientifique d'Orsay, n ° 3193 (1986). [D J] G. D a v i d & J . - L . J o u r n 6 A boundedness criterion for generalized Calder6nZygmund operators. Ann. Math. 120 (1984), 371-397. [DJS] G . D a v i d , J . - L . J o u r n 6 & S. S e m m e s Op6rateurs de CalderSn-Zygmund, fonctions para-accr6tives et interpolation.

L . J o u r n 6 A boundedness criterion for generalized Calder6nZygmund operators. Ann. Math. 120 (1984), 371-397. [DJS] G . D a v i d , J . - L . J o u r n 6 & S. S e m m e s Op6rateurs de CalderSn-Zygmund, fonctions para-accr6tives et interpolation. Revista Matematlca Iberoamericana 1 (1985), 1-56. [LM] P. G . L e m a r i ~ K= Y . M e y e r Ondelettes et bases hilbertiennes. Revista Matematica Iberoamericana 2 (1986), 1-18. [M] Y . M e y e r Ondelettes et op~rateurs. Paris, Hermann, 1990. 50 IS] S.

I1 s'agit d ' u n op~rateur lin~ake (borne), d~fini sur P = C ~ ( I R ~) et g valeurs dans son dual P~, pour lequel il existe un noyau standard (la notion 40 est dEfinie plus bas) tel que (1) = / / K(x,y)f(y)g(x)dydx d~s que f et g sont des fonctions-test dont les supports sont disjoints. (On note < T f, g > l'effet de la distribution Tf sur la fonction g). Un noyau standard sur ]R ~ est une fonction IRn x ~ \ { x = y}, telle que I K(x,Y) K(x,y), I<_ C l x- dEfinie et continue sur y l -'~ et (3) pour I K ( x , y ) - K ( x ' , y ) l + l K(y,~:) - K ( y , z ' ) l~ C l x - x,x',y E IR '~ tels que !

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