Différentiation des capacités et des intégrales de Choquet

For any subadditive capacity κ on R dominated by a Radon measure, we show that lim κ (χ − δ, χ + ε]/(δ + ε) = d_κ (χ) exists for a.a. χ, as δ + ε → 0. Moreover, the Choquet integrals of any positive mesurable g satisfy

     

Sur quelques propriétés des zéros des polynomes orthogonaux

Résumé L'au. démontre des relations nouvelles entre les zéros des polynomes orthogonaux. à Giovanni Sansone pour son 70^ème anniversaire.     

Sur les sous-variétés des tores

In Invent. Math. 126 (2000), pp. 513–545, we gave a proof of Lang's conjecture on Abelian varieties leading to an effective bound for the number of translates involved. We show here that the method can be extended to give a similar statement for the Mordell–Lang plus Bogomolov theorem proven by B. Poonen and independently by S. Zhang. We deal in detail with tori for which effective results have been obtained by J.-H. Evertse and H. P. Schlickewei; we improve on these mainly by providing polynomial bounds in the degree instead of doubly exponential ones. We also state a theorem for Abelian varieties. In both cases the strategy of proof is based on the approach of Mumford and Vojta–Faltings–Bombieri together with an effective Bogomolov property and therefore does not rely on either equidistribution nor subspace theorem arguments.     

Sur la cohomologie LP des variétés

The main purpose of this Note is to indicate vanishing and non vanishing theorems for L^p cohomology of riemannian manifolds, especially when the dimension is half the dimension of Riemannian symmetric space.     

Densité des zéros des transformés de Lévy itérés d'un mouvement brownien

The Lévy transform of a Brownian motion B is the Brownian motion $\text{B′}{}_{\mathrm{t}}\text{=∫}{}_0{}^{\mathrm{t}}\text{sgn}\text{B}{}_{\mathrm{s}}\text{d}\text{B}{}_{\mathrm{s}}$; denote by Bⁿ the Brownian motion obtained from B by iterating n times the Lévy transform. We establish that the set of all instants t such that B_tⁿ=0 for some n, is a.s. dense in the time-axis $\text{R}{}_{\mathrm{+}}$. To cite this article: M. Malric, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Propriétés probabilistes des processus GARCH périodiques

This Note examines the probabilistic structure of a GARCH-type stochastic difference equation with periodically time-varying parameters. We propose necessary and sufficient conditions ensuring the existence of stationary solutions, geometrically ergodic (in the periodic sense) and having finite higher-order moments. To cite this article: A. Bibi, A. Aknouche, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Une caractérisation des variétés complexes compactes parallélisables admettant des structures affines

We classify complex compact parallelizable manifolds which admit flat torsion free holomorphic affine connections. We exhibit complex compact manifolds admitting holomorphic affine connections, but no flat torsion free holomorphic affine connections. To cite this article: S. Dumitrescu, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Enveloppe d'holomorphie locale des variétés CR et élimination des singularités pour les fonctions CR intégrables

Let M be a locally embeddable CR manifold and Φ ⊂M be a closed set. We give sufficient conditions in order that L_loc¹ functions on M which are CR on M #x003A6; are CR on M.     

Semi-groupes sous-Markoviens engendrés par des opérateurs matriciels

We characterize generators of sub-Markovian semigroups onL ^p () by a version of Kato's inequality. This will be used to show (under precise assumptions) that the semigroup generated by a matrix operatorA=(A _ij )_1i,jn on (L ^p ()) ⁿ is sub-Markovian if and only if the semigroup generated by the sum of each rowA _i 1+...+A _in (1in), is sub-Markovian. The corresponding result on (C ₀(X)) ⁿ characterizes dissipative operator matrices.

     

Comparaison des semi-groupes et des résolvantes d'ordre α associés à des opérateurs différentiels de type divergence

We prove that the densities of the semi-groups of order , 0<<1 associated with differential operators of second order and of divergence type, and the density of Riesz semi-groups of order are comparables.We give a necessary and sufficient condition such that the semi-group of order and its resolvent family and their perturbated with a nonnegative and regular Radon measure are comparables.When =1, we prove that the semi-group of brownian motion and its perturbated with a radial and nonnegative measure are comparables if and only if the measure generates a bounded potential, but the result is not true if the measure is not radial.

Ce travail est soutenu par la Fondation Nationale pour la Recherche Scientifique.     

Propriétés asymptotiques d'estimateurs convergents des quantiles conditionnels

We state sufficient conditions for asymptotic normality of convergent estimates of the conditional quantiles, irrespective of data dependence, and give an application to α-mixing stationary processes, under optimal conditions. As an application, we use asymptotic normality to construct confidence bands for predictors based on nonparametric estimates of the conditional median.     

Lemmes de décomposition appliqués à des inégalités de type Hardy–Sobolev

Decomposition (or concentration-compactness) lemmas have already shown their efficience in order to show existence of minimizers or ground state solutions. The aim of this paper is to apply new version of these lemmas to minimisation problems involving Hardy–Sobolev type inequalities on a specific class of unbounded domains. More precisely, we shall find ground state solution for the following quotient, where value of real numbers ,b,q and are given.

Une série génératrice des formes paraboliques de Maass

A certain periodic function F_μ,ν(z), an eigenfunction of the Laplacian on the upper half-plane with respect to z depending on some parameters μ, ν, is not automorphic, but the function μ → F_μ,ν(z)−F_μ,ν(−1/0 extends to a larger domain than the function F_μ,ν(z) itself. Consequently, at the poles of this latter function of μ, the coefficients of the polar parts provide non-analytic modular forms: all Maass cusp forms are finite linear combinations of forms obtained in this way, allowing the second parameter ν to vary