Proprietes generiques de processus croises

LetS _φ be the skew product transformation(x, g)↦(Sx, gφ(x)) defined on Ω×G, where Ω is a compact metric space,G a compact metric group with its Haar measureh. IfS is a μ-continuous transformation where μ is a Borel measure on Ω, ergodic with respect toS, we study the setE ₀ of μ-continuous applications φ:Ω→G such that μ⩀h is ergodic (with respect toS _φ). For example,E ₀ is residual in the group of μ-continuous applications from Ω toG with the uniform convergence topology. We also study the weakly mixing case. Some arithmetic applications are given.     

Ideaux de polynomes et ideaux de valeurs

Let B be the ring of integral valued polynomials over a noetherian domain A. We study in which case finitely generated ideals of B are uniquely determined by their ideals of values at each element of A. We give necessary and sufficient conditions which are verified for example when A is any ring of integers of an algebraic number field, such that each quotient ring Am with respect to a maximal ideal m is analytically irreducible.     

Idéaux primitifs induits dans les produits croisés

Let an amenable second countable locally compact group G act continuously on a separable C¹-algebra A: the structure of the prime ideal space of the crossed product $\text{C}{}^1\text{(G, A)}$ is investigated without any restricting hypothesis on the action of G.     

Sur certains ensembles de Salem

Sans résuméDédié au ProfesseurG. Alexits pour son 70^e anniversaire     

Sur la factorisation de certains multiplicateurs

Sans résumé     

Sur les nombres de classes de certains corps quadratiques

Sans résumé     

Calcul fonctionnel dans certains espaces de Lizorkin-Triebel

Sans résumé     

Sur certains semi-groupes de matrices non negatives

Sans résumé     

Renormage de certains espaces d'opérateurs

Sans résumé     

Comportement moyen du cardinal de certains ensembles de facteurs premiers

Letn be a positive integer andS _n a particular set of prime divisors ofn. We establish the average order off(n) wheref(n) stands for the cardinality ofS _n . Thek-ary,k-free, semi-k-ary prime factors ofn are some of the classes of prime divisors studied in this paper.

     

Sur la monogeneite de l'anneau des entiers de certains corps de rayon

Sans résumé     

Sur la laminarité de certains courants

We show that a sequence of smooth analytic curves of the unit ball of the complex plane, for which the genus is bounded by the area, converges to a lamination in a weak sense.     

Une propriete arithmetique de certains operateurs differentiels

Define and let L(D)=a_i(x)Dⁱ[x][D] be a linear differential operator with polynomial coefficients. G. POLYA for L(D)=D and D. CANTOR for L(D)=P(xD), P[x] proved that if u[[x]] is such that L(D)(u) is a rational function, then u is also a rational function.In this paper, we introduce a new class of linear differential operators with the same property.     

Intersection de produits fibres et formule de la dimension

We generalize classical results of tranfer properties to finite intersections of pullbacks at various maximal ideals of a domain T; we also get new transfer results on the dimension formula.