We study the connections between the uniform exponential dichotomy of a discrete linear skew-product semiflow and the uniform admissibility of the pair $(c_{0}(\n,X),c_{00}(\n, X))$. We give necessary and sufficient conditions for uniform exponential dichotomy of linear skew-product semiflows in terms of the uniform admissibility of the pairs $(c_{0}(\n, X),c_{00}(\n, X))$ and $(C_0(\r, X),$ $C_{00}(\r, X))$, respectively. We generalize a dichotomy theorem due to Van Minh, Räbiger and Schnaubelt for the case of linear skew-product semiflows.

Cet article traite le problème de la stabilité exponentielle d'un système composé de deux échangeurs thermiques à contre-courant. Celui-ci sera formulé sous une forme abstraite de système hyperbolique à coefficients variables (d'espace), bornés mais discontinus. En utilisant la méthode classique de régularisation et la méthode des caractéristiques, on montre dans un cadre assez large la stabilité exponentielle d'une classe de systèmes hyperboliques à coefficients dans $L^{\infty}$. Ce résultat est ensuite appliqué à notre système d'échangeurs thermiques pour établir sa stabilité exponentielle.

This paper deals with exponential stability for a large class of first order symmetric hyperbolic linear systems with $L^{\infty}$ space variable coefficients. By using the classical method of regularization and the method of characteristics, we prove that such systems are exponentially stable without any smoothness assumption on the coefficients. Since our motivation comes from a coupled heat exchangers system, we give an interesting application to this physical system met in chemical engineering.

Here we prove that a reduced curve $X \subset {\bf {P}}^N$ either canonically embedded or with a high degree complete embedding is arithmetically Cohen - Macaulay.

We consider the space {\bf $L_\Omega ^p\left( R^n\right) ,$ }$1\leq p < +\infty ,$ where $\Omega $ is a family of weights. We give a necessary and sufficient condition, on $\Omega ,$ for {\bf $L_\Omega ^p\left( R^n\right) $ } to be locally m-convex algebra. Fundamental properties of this algebra are also obtained.

Nous mettons en évidence des propriétés géométriques de fonctions convexes semi-continues inférieurement et nous caractérisons les espaces de Banach ayant la propriété de Radon-Nikodym par des propriétés géométriques des fonctions convexes qui y sont définies.

We give geometrical properties of lower semi-continuous convex functions and we obtain a characterization of Banach spaces with the Radon-Nikodym property using geometrical properties of convex functions defined on Banach spaces.

Dans ce travail nous exposons d'abord une méthode de réduction développée par R.A. Smith, puis nous l'appliquons pour généraliser le théorème de Cartwright à une classe d'équations différentielles fonctionnelles à retard. Nous montrons, pour ces équations, que les solutions presque-périodiques, lorsqu'elles existent, sont quasi-périodiques.

In this work we first explain a reduced method developed by R.A. Smith, then we apply it to extend a theorem due to M. Cartwright to a class of autonomous retarded functional differential equations. We show, for these equations, that the almost-periodic solutions, when they exist, are quasi-periodic.

We give some criterions to establish connectedness for the geometric representation domain of substitutions of Pisot type, unimodular and satisfying the strong coincidence condition (PUC substitutions).

We propose a reduction procedure for symplectic connections with symmetry. This is applied to coadjoint orbits whose isotropy is reductive.

Toeplitz operators on Hardy spaces $H\sp{p} $ have been studied extensively during the past 40 years or so. An important special case is that of the operators of multiplication by a bounded analytic function $\f $: $M\sb{\f}(f)=\f f $ (analytic Toeplitz operators). However, many results about them are either only formulated in the case $p=2 $, or are not so easy to find in an explicit form. The purpose of this paper is to give a complete overview of the spectral theory of these analytic Toeplitz operators on a general space $H\sp{p} $, $1\le p <\infty $. The treatment is kept as elementary as possible, placing a special emphasis on the key role played by certain extremal functions related to the Poisson kernel.

We obtain the characteristic numbers of the variety of non degenerate cuspidal plane cubics in $\mathbb P^3$, namely, the non-zero intersection numbers which arise from considering 10 (possibly repeated) conditions from among the following: $P$, that the cuspidal cubic go through a point; $\nu$, that the cuspidal cubic intersect a line; and $\rho$, that the cuspidal cubic be tangent to a plane. In order to reach this goal, we consider a suitable compactification of the variety of non degenerate cuspidal plane cubics in $\mathbb P^3$ and we calculate, using several degeneration formulae, some of its non-zero intersection numbers, including all the characteristic ones.

The aim of this paper is the study of some transformations in the Laguerre-Hahn affine class that do not preserve the class. Under very general conditions, we establish that the second kind functional associated with a Laguerre-Hahn affine functional does not belong to the Laguerre-Hahn affine class. The transformations related to the associated polynomials and quadratic decomposition of a sequence of orthogonal polynomials are also considered.

L'objectif de ce travail est de généraliser le calcul fonctionnel harmonique et ses applications aux algèbres de Banach alternatives involutives.

The purpose of this paper is to extend the harmonic functional calculus and their applications to involutory alternative Banach algebras.