Measures with real spectra.
Mesures de Lévy et fonctions de Lévy générales Applications à la décomposition de Lévy-Khintchine
Mesures invariantes et mesures quasi-invariantes
Mesures spectrales de Walsh associées à certaines suites arithmétiques
On associe à certaines suites de nombres complexes une mesure borélienne positive sur le tore dont la transformée de Fourier-Walsh est une suite de moyennes liées à . La nature de (discrète, continue) est discutée dans quelques cas : suites presque-périodiques et certaines suites arithmétiques.
Mesures ε-idempotentes de norme bornée
Moments of probability measures on a group.
Multiplier semigroups and weakly almost periodic measures on foundation semigroups.
Necessary condition for measures which are multipliers
Let be a locally compact group and the left Haar measure on . Given a non-negative Radon measure , we establish a necessary condition on the pairs for which is a multiplier from to . Applied to , our result is stronger than the necessary condition established by Oberlin in [14] and is closely related to a class of measures defined by Fofana in [7].When is the circle group, we obtain a generalization of a condition stated by Oberlin [15] and improve on it in some cases.
Negatively curved groups and the convergence property. II: Transitivity in negatively curved groups.
Non singular transformations and spectral analysis of measures
Non-archimedean (uniformly) continuous measures on homogeneous spaces
Norm- and weak-continuity of translations of measures: A counterexample.
On a Formula for Haar Measure in Compact Groups.
On a joint generalization of Cauchy's and d'Alembert's functional equations.
On a Limit Theorem of Measures.
On Beurling measure algebras
We show how the measure theory of regular compacted-Borel measures defined on the -ring of compacted-Borel subsets of a weighted locally compact group provides a compatible framework for defining the corresponding Beurling measure algebra , thus filling a gap in the literature.
On certain regularity properties of Haar-null sets
Let X be an abelian Polish group. For every analytic Haar-null set A ⊆ X let T(A) be the set of test measures of A. We show that T(A) is always dense and co-analytic in P(X). We prove that if A is compact then T(A) is dense, while if A is non-meager then T(A) is meager. We also strengthen a result of Solecki and we show that for every analytic Haar-null set A, there exists a Borel Haar-null set B ⊇ A such that T(A)∖ T(B) is meager. Finally, under Martin’s Axiom and the negation of Continuum Hypothesis,...
On compact transformation groupoids
On concentrated probabilities on non locally compact groups
Let be a Polish group with an invariant metric. We characterize those probability measures on so that there exist a sequence and a compact set with for all .
On continuity of measurable group representations and homomorphisms
Let G be a locally compact group, and let U be its unitary representation on a Hilbert space H. Endow the space ℒ(H) of bounded linear operators on H with the weak operator topology. We prove that if U is a measurable map from G to ℒ(H) then it is continuous. This result was known before for separable H. We also prove that the following statement is consistent with ZFC: every measurable homomorphism from a locally compact group into any topological group is continuous.