Corrigendum and addendum to the paper "In general, Bernoulli convolutions have independent powers", Studia Math. 47 (1973), pp. 141-152
Coshape-invariant functors and Mackey's induced representation theorem
Countable products of LCA groups: their closed subgroups, quotients and duality properties
Courbure et sous-ensembles de courbes rectifiables dans le groupe de Heisenberg
Nous présentons une condition suffisante pour qu’un compact dans le groupe de Heisenberg (muni de sa structure de Carnot-Carathéodory) soit contenu dans une courbe rectifiable. Cette condition est aussi nécessaire dans le cas de courbes régulières (en particulier, des géodésiques) et elle est inspirée du lemme géométrique faible du à Peter Jones dans le cas euclidien. Cette note repose sur l’exposé fait par le troisième auteur (au Séminaire X-EDP) et décrit les principaux résultats de l’article...
Covering theorems for uniqueness and extended uniqueness sets
Criterion for proper actions on homogeneous spaces of reductive groups.
Critical constants for recurrence of random walks on -spaces
We introduce the notion of a critical constant for recurrence of random walks on -spaces. For a subgroup of a finitely generated group the critical constant is an asymptotic invariant of the quotient -space . We show that for any infinite -space . We say that is very small if . For a normal subgroup the quotient space is very small if and only if it is finite. However, we give examples of infinite very small -spaces. We show also that critical constants for recurrence can be used...
Crofton formulae and geodesic distance in hyperbolic spaces.
Croissance polynomiale et périodes des fonctions harmoniques
Cross Sections and an Explicit Formula for the Plancherel Measure on a Nilpotent Lie Group.
Cyclic subspaces for unitary representations of LCA groups; generalized Zak transform
We just published a paper showing that the properties of the shift invariant spaces, ⟨f⟩, generated by the translates by ℤⁿ of an f in L²(ℝⁿ) correspond to the properties of the spaces L²(𝕋ⁿ,p), where the weight p equals [f̂,f̂]. This correspondence helps us produce many new properties of the spaces ⟨f⟩. In this paper we extend this method to the case where the role of ℤⁿ is taken over by locally compact abelian groups G, L²(ℝⁿ) is replaced by a separable Hilbert space on which a unitary representation...
Cyclic Vectors for Representations of Locally Compact Groups.
D'Alembert's equation and spherical functions.
D'Alembert's functional equation on compact groups.
Darstellungen von Liegruppen und Approximationsprozesse auf Banachräumen.
Das Syntheseproblem für invariante Distributionen.
Decomposable multipliers and applications to harmonic analysis
For a multiplier on a semisimple commutative Banach algebra, the decomposability in the sense of Foiaş will be related to certain continuity properties and growth conditions of its Gelfand transform on the spectrum of the multiplier algebra. If the multiplier algebra is regular, then all multipliers will be seen to be decomposable. In general, an important tool will be the hull-kernel topology on the spectrum of the typically nonregular multiplier algebra. Our investigation involves various closed...
Decomposition of analytic measures on groups and measure spaces
We consider an arbitrary locally compact abelian group G, with an ordered dual group Γ, acting on a space of measures. Under suitable conditions, we define the notion of analytic measures using the representation of G and the order on Γ. Our goal is to study analytic measures by applying a new transference principle for subspaces of measures, along with results from probability and Littlewood-Paley theory. As a consequence, we derive new properties of analytic measures as well as extensions of previous...
Decomposition of Positive Definite Functions Defined on a Neighbourhood of the Identity.
Decreasing rearrangements and of the Bohr group