Power-monotone sequences and Fourier series with positive coefficients.
Power-monotone sequences and integrability of trigonometric series.
Practice of operator relationships in symbolical calculus.
Prediction for Two Processes and the Nehari Problem.
Preservation of Lipschitz class by the iterated conjugate operator
Prevalence of some known typical properties.
Principe d’Heisenberg et fonctions positives
On décrit un problème naturel concernant la transformation de Fourier. Soient , deux fonctions associées par celle-ci, positives pour et nulles en zéro. Quelle est la borne inférieure pour ? En dimension supérieure, même question, l’intervalle étant remplacé par la boule de rayon . On montre l’existence d’une borne inférieure strictement positive, qui est estimée en fonction de la dimension. La dernière section montre que cette question est naturellement liée à la théorie des fonctions zêta....
Principe d'incertitude, bases hilbertiennes et algèbres d'opérateurs
Probabilistic well-posedness for the cubic wave equation
The purpose of this article is to introduce for dispersive partial differential equations with random initial data, the notion of well-posedness (in the Hadamard-probabilistic sense). We restrict the study to one of the simplest examples of such equations: the periodic cubic semi-linear wave equation. Our contributions in this work are twofold: first we break the algebraic rigidity involved in our previous works and allow much more general randomizations (general infinite product measures v.s. Gibbs...
Problèmes de complémentation de sons-algèbre dans l'algèbre des séries de Fourier en deux variables absolument convergentes
Problèmes de pseudo-périodicité
Problems from probability theory
Problems on averages and lacunary maximal functions
We prove three results concerning convolution operators and lacunary maximal functions associated to dilates of measures. First we obtain an H¹ to bound for lacunary maximal operators under a dimensional assumption on the underlying measure and an assumption on an regularity bound for some p > 1. Secondly, we obtain a necessary and sufficient condition for L² boundedness of lacunary maximal operator associated to averages over convex curves in the plane. Finally we prove an regularity result...
Product rule and chain rule estimates for the Hajłasz gradient on doubling metric measure spaces
We use the Calderón Maximal Function to prove the Kato-Ponce Product Rule Estimate and the Christ-Weinstein Chain Rule Estimate for the Hajłasz gradient on doubling measure metric spaces.
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.
Proof of a Conjecture on the Supports of Wigner Distributions.
Proper moving average representations and outer functions in two variables.
Properties of bounded orthonormal spline bases
Properties of certain improper integrals
Properties of extremal sequences for the Bellman function of the dyadic maximal operator
We prove a necessary condition that has every extremal sequence for the Bellman function of the dyadic maximal operator. This implies the weak- uniqueness for such a sequence.