Nous définissons un produit renormalisé par ondelettes qui améliore, dans certains cadres fonctionnels, les propriétés du produit usuel de deux fonctions. Grâce à cette technique de renormalisation du produit nous obtenons une démonstration par ondelettes d'une version précisée du théorème du Jacobien. Finalement nous établissons le lien entre ce produit renormalisé par ondelettes et les paraproduits de J.M. Bony.

In this paper, a new class of Gaussian field is introduced called Lacunary Fractional Brownian Motion. Surprisingly we show that usually their tangent fields are not unique at every point. We also investigate the smoothness of the sample paths of Lacunary Fractional Brownian Motion using wavelet analysis.

In this paper, a new class of Gaussian field is introduced called Lacunary Fractional Brownian Motion. Surprisingly we show that usually their tangent fields are not unique at every point. We also investigate the smoothness of the sample paths of Lacunary Fractional Brownian Motion using wavelet analysis.

Nous étudons sur des exemples significatifs l’intersection entre le traitement du signal et l’analyse fonctionnelle.

Multiplicatively invariant (MI) spaces are closed subspaces of L²(Ω, ) that are invariant under multiplication by (some) functions in $L^{\infty }\left(\Omega \right)$; they were first introduced by Bownik and Ross (2014). In this paper we work with MI spaces that are finitely generated. We prove that almost every set of functions constructed by taking linear combinations of the generators of a finitely generated MI space is a new set of generators for the same space, and we give necessary and sufficient conditions on the linear...

We present, discuss and apply two reiteration theorems for triples of quasi-Banach function lattices. Some interpolation results for block-Lorentz spaces and triples of weighted $L_p$-spaces are proved. By using these results and a wavelet theory approach we calculate (θ,q)-spaces for triples of smooth function spaces (such as Besov spaces, Sobolev spaces, etc.). In contrast to the case of couples, for which even the scale of Besov spaces is not stable under interpolation, for triples we obtain stability...

The paper deals with local means and wavelet bases in weighted and unweighted function spaces of type $B_{pq}^s$ and $F_{pq}^s$ on ℝⁿ and on ⁿ.

The paper deals with local means and wavelet bases in function spaces of Besov and Triebel-Lizorkin type with local Muckenhoupt weights.

We consider two standard group representations: one acting on functions by translations and dilations, the other by translations and modulations, and we study local Toeplitz operators based on them. Local Toeplitz operators are the averages of projection-valued functions $g\mapsto P_{g,\varphi }$, where for a fixed function ϕ, $P_{g,\varphi }$ denotes the one-dimensional orthogonal projection on the function $U_g\varphi$, U is a group representation and g is an element of the group. They are defined as integrals ${ʃ}_W{P}_{g,\varphi }dg$, where W is an open, relatively...

Orthonormal bases of wavelet packets constitute a powerful tool in signal compression. It has been proved by Koifman, Meyer and Wickerhauser that many wavelet packets wn suffer a lack of frequency localization. Using the L1-norm of the Fourier transform ^wn as localization criterion, they showed that the average 2-jΣn=02j-1 ||^wn||L1 blows up as j goes to infinity. A natural problem is then to know which values of n create this blow-up in average. The present work gives an answer to this question,...