Sur les représentations des groupes de Lie réductifs non connexes.
Sur les représentations unitaires d'un groupe
Sur l'espace de Banach engendré par les coefficients d'une représentation unitaire
Tensor products and p-induction of representations on Banach spaces.
In this paper we obtain Lp versions of the classical theorems of induced representations, namely, the inducing in stages theorem, the Kronecker product theorem, the Frobenius Reciprocity theorem and the subgroup theorem. In doing so we adopt the tensor product approach of Rieffel to inducing.
The asymptotics of spherical functions and the central limit theorem on symmetric cones
We prove a central limit theorem for certain invariant random variables on the symmetric cone in a formally real Jordan algebra. This extends form the previous results of Richards and Terras on the cone of real positive definite matrices.
The Clebsch-Gordan coefficients with respect to various bases for unitary and orthogonal representations of and .
The dual space of precompact groups
For any topological group the dual object is defined as the set of equivalence classes of irreducible unitary representations of equipped with the Fell topology. If is compact, is discrete. In an earlier paper we proved that is discrete for every metrizable precompact group, i.e. a dense subgroup of a compact metrizable group. We generalize this result to the case when is an almost metrizable precompact group.
The Fourier-Stieltjes algebra of a semisimple group
The plancherel formula for group extensions II
The singularity of orbital measures on compact Lie groups.
We find the minimal real number k such that the kth power of the Fourier transform of any continuous, orbital measure on a classical, compact Lie group belongs to l2. This results from an investigation of the pointwise behaviour of characters on these groups. An application is given to the study of Lp-improving measures.
The size of characters of compact Lie groups
Pointwise upper bounds for characters of compact, connected, simple Lie groups are obtained which enable one to prove that if μ is any central, continuous measure and n exceeds half the dimension of the Lie group, then . When μ is a continuous, orbital measure then is seen to belong to . Lower bounds on the p-norms of characters are also obtained, and are used to show that, as in the abelian case, m-fold products of Sidon sets are not p-Sidon if p < 2m/(m+1).
The Type Structure of the Regular Representation of a Locally Compact Group.
The Unitary Dual of GI (3, IR) and GI (4, IR).
The weakly almost periodic compactification: Another approach.
Time Dependent Perturbations and Scattering of Strongly Continuous Groups on Banach Spaces.
Transformation de Riesz pour les semi-groupes symétriques. Première partie : étude de la dimension 1
Transformation de Riesz pour les semi-groupes symétriques. Seconde partie : étude sous la condition
Une ébauche d'une théorie générale des fonctions définies-négatives
Une remarque sur les inégalités de Littlewood-Paley sous l’hypothèse
Uniformly bounded representations of free groups.