Base d'ondelettes sur les groupes de Lie stratifiés
Continuité sur les espaces de Besov des opérateurs définis par des intégrales singulières
On donne un critère très simple de continuité des opérateurs définis par des intégrales singulières sur les espaces de Besov homogènes pour . Quelques exemples, utilisant notamment l’opérateur de paraproduit, illustrent ensuite l’emploi de ce critère.
A remark on the div-curl lemma
We prove the div-curl lemma for a general class of function spaces, stable under the action of Calderón-Zygmund operators. The proof is based on a variant of the renormalization of the product introduced by S. Dobyinsky, and on the use of divergence-free wavelet bases.
Ondelettes generalisées et fonctions d'échelle à support compact.
We show that to any multi-resolution analysis of L(R) with multiplicity d, dilation factor A (where A is an integer ≥ 2) and with compactly supported scaling functions we may associate compactly supported wavelets. Conversely, if (Ψ = A Ψ (Ax - k)), 1 ≤ ε ≤ E and j, k ∈ Z, is a Hilbertian basis of L(R) with continuous compactly supported mother functions Ψ, then it is provided by a multi-resolution analysis with dilation factor A, multiplicity d = E / (A - 1) and with compactly supported scaling...
Fonctions a support compact dans les analyses multi-résolutions.
The main topic of this paper is the study of compactly supported functions in a multi-resolution analysis and especially of the minimally supported ones. We will show that this class of functions is stable under differentiation and integration and how to compute basic quantities with them.
Projecteurs invariants, matrices de dilatation, ondelettes et analyses multi-résolutions.
We show that (bi-orthogonal) wavelet bases associated to a dilation matrix which is compatible with integer shifts are generally provided by a multi-resolution analysis. The proof is done by studying the projectors which commute with integer shifts.
Analyses multi-résolutions non orthogonales, commutation entre projecteurs et derivation et ondelettes vecteurs à divergence nulle.
The notion of non-orthogonal multi-resolution analysis and its compatibility with differentiation (as expressed by the commutation formula) lead us to the construction of a multi-resolution analysis of L(R) which is well adapted to the approximation of divergence-free vector functions. Thus, we obtain unconditional bases of compactly supported divergence-free vector wavelets.
Fonctions d'échelle interpolantes, polynômes de Bernstein et ondelettes non stationnaires.
The theory of convergence for (non-stationary) scaling functions and the approximation of interpolating scaling filters by means of Bernstein polynomials, allow us to construct a non-stationary interpolating scaling function with interesting approximation properties.
Sur l'existence des analyses multi-résolutions en théorie des ondelettes.
On montre qu'une base d'ondelettes (ψ) de L(R) avec une fonction mère ψ höldérienne à support compact provient nécessairement d'une analyse multi-résolution. La fonction-père φ a alors la même régularité que la fonction ψ et peut être choisie à support compact.
Point fixe d'une application non contractante.
We study a multilinear fixed-point equation in a closed ball of a Banach space where the application is 1-Lipschitzian: existence, uniqueness, approximations, regularity.
Quelques remarques sur les équations de Navier-Stokes dans
Nous présentons un résultat d’existence globale de solutions faibles des équations de Navier-Stokes dans pour des données initiales d’énergie infinie.
Remarques sur la formule sommatoire de Poisson
It is well known that the condition “f ∈ L¹ and f̂ ∈ L¹” is not sufficient to ensure the validity of the Poisson summation formula ∑f(k) = ∑f̂(k). We discuss here a stronger condition " and " and see for which values of a and b the condition is sufficient.
Ondelettes et bases hilbertiennes.
The phase of the Daubechies filters.
We give the first term of the asymptotic development for the phase of the N-th (minimum-phased) Daubechies filter as N goes to +∞. We obtain this result through the description of the complex zeros of the associated polynomial of degree 2N+1.
Unicité dans L(R) et d'autres espaces fonctionnels limites pour Navier-Stokes.
The main result of this paper is the proof of uniqueness for mild solutions of the Navier-Stokes equations in L(R). This result is extended as well to some Morrey-Campanato spaces.
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