Théorie du potentiel sur les produits infinis et les groupes localement compacts

Let F. be a connected amd locally connected locally compact group having a countable basis for its topology. Does E admit a translation invariant Brelot harmonic sheaf? For which E does the elliptic Bauer theory coincides with the Brelot theory for all invariant harmonic elliptic sheaves? This note announces the following solutions: (a) Any E carries invariant Brelot harmonic sheaves; (b) Any invariant elliptic Bauer harmonic elliptic sheaf is a Brelot sheaf if and only if E is a finite dimensional Lie group. These results are obtained by studying product diffusions on infinite products of manifolds. e.g.. compacts Lie groups.     

Sur les courbes de distribution des probabilités

Sans résumé     

Une caractérisation de l'algèbre de Fourier pour certains groupes localement compacts

Let G be a separable locally compact group with type-I left regular representation, $\stackrel{?}{G}$ its dual and $A(G)$ its Fourier algebra. We prove an analogue of Parseval's theorem and that the mapping

$T?u(x):=\underset{\stackrel{?}{G}}{\int }Tr[T(\pi )\pi {(x)}^{?1}]{\mathrm{d}}_{\mu }(\pi )$

is an isometric isomorphism of Banach spaces from $L^1(\stackrel{?}{G})$ onto $A(G)$.     

Quelques remarques sur les actions analytiques des réseaux des groupes de Lie de rang supérieur

All the actions considered here are (real) analytic. Let г be a subgroup of finite index of SL(n,). We prove, in particular, the (global) homotopical rigidity, for both its standard affine action on the torus T^a (n ≥ 3), and its standard projective action on the sphere Sⁿ⁻¹ (n, ≥ 4).     

Flot horosphérique des repères sur les variétés hyperboliques de dimension 3 et spectre des groupes kleiniens

Let Γ be a Kleinian group. The action of the upper unipotent subgroup by right multiplication on Γ\PSL(2,ℂ) is conjugated to a two-dimensional flow on the frame bundle of the hyperbolic manifold Γ\³. We show that the topology of orbits (compactness, divergence, density) is analogous to the topology of the horospherical foliation on hyperbolic manifolds. In order to study dense orbits, we prove a result of "non-arithmeticity" of the spectrum of Kleinian groups. Received: 8 January 2002     

Processus de Lévy autosimilaires sur les groupes de Lie

In this Note we study the global autosimilarity property of Lévy processes on Lie groups.     

Cohomologie des groupes linéaires,K-théorie de Milnor et groupes de Witt

We construct some remarkable classes in the cohomology of linear groups.     

Sur les groupes de difféomorphismes des variétés différentiables

Résumé Nous établissons ici deux conditions. nécessaires et suffisantes, pour qu'une algèbre deLie de champs de vecteurs tangents à une variété différentiable V, engendre un groupe global de difféomorphismes de V. à M. Enrico Bompiani pour son Jubilé scientifique.     

Moyennabilité des groupes dénombrables et actions sur les espaces de Cantor

We answer a question of R. Grigorchuk by showing the following characterization: for a countable group Γ to be amenable, it is necessary and sufficient that any continuous action of Γ on the Cantor set has an invariant probability measure. The proof uses an easy variation of a classical result of Alexandroff and Urysohn: any metrisable Γ-space is an equivariant surjective image of a Γ-Cantor set.     

Recherches sur la convergence des séries de fourier

Sans résumé     

Théorèmes sur les groupes de substitutions

Sans résumé     

Nombres de Tamagawa des groupes réductifs quasi-connexes

We define Tamagawa numbers for quasi-connected linear algebraic groups. This category of non-connected linear algebraic groups occurs naturally in the stabilization of the Arthur-Selberg trace formula. An expression for their Tamagawa numbers, needed for the stabilization process, is given in term of cohomological invariants generalizing results of Ono, Sansuc, Kottwitz and Kottwitz & Shestad. Received: 7 March 2000     

Nouvelle démonstration de théorèmes sur des séries de points correspondants sur deux courbes

Sans résumé