Sets of interpolation and small p sets
Sets of interpolation for Fourier transforms of bimeasures
Sets of p-multiplicity in locally compact groups
We initiate the study of sets of p-multiplicity in locally compact groups and their operator versions. We show that a closed subset E of a second countable locally compact group G is a set of p-multiplicity if and only if is a set of operator p-multiplicity. We exhibit examples of sets of p-multiplicity, establish preservation properties for unions and direct products, and prove a p-version of the Stone-von Neumann Theorem.
Sets of uniqueness
Sidon sets and Bohr cluster points
It is shown that a Sidon set cannot have an integer cluster point in the Bohr topology.
Sidon sets and -sets
Sidon sets and Riesz products
Let be a compact abelian group and the dual group. It is shown that if is a Sidon set, then the interpolating measures on can be obtained as mean of Riesz products. If is a Sidon set tending to infinity, is of first type. Our approach yields in fact elementary proofs of certain characterizations of Sidonicity obtained in G. Pisier, C.R.A.S., Paris Ser. A, 286 (1978), 1003–1006 – Math. Anal. and Appl., Part B, Advances in Math., Suppl. Sts. vol. 7, 685-726 – preprint, using random Fourier...
Sidon sets in Rn.
Sidon Sets on Compact Groups.
Sidonicity in compact, abelian hypergroups
Sigma-idéaux polaires et ensembles d'unicité dans les groupes abéliens localement compacts
On étend au cadre des groupes abéliens localement compacts certains résultats obtenus notamment par G. Debs, R. Kaufman, A. Kechris, A. Louveau et J. Saint Raymond sur la structure des fermés d’unicité et d’unicité au sens large du cercle unité. On montre également que de très nombreuses familles de compacts issues de l’Analyse Harmonique sont exactement de troisième classe dans la hiérarchie de Baire. Comme application, on donne une démonstration simple de l’existence d’ensembles de Dirichlet qui...
Some natural families of M-ideals.
Some remarks on quasi-Cohen sets
We are interested in Banach space geometry characterizations of quasi-Cohen sets. For example, it turns out that they are exactly the subsets E of the dual of an abelian compact group G such that the canonical injection is a 2-summing operator. This easily yields an extension of a result due to S. Kwapień and A. Pełczyński. We also investigate some properties of translation invariant quotients of L¹ which are isomorphic to subspaces of L¹.
Some remarks on sets of uniform convergence
Some results on Kronecker, Dirichlet and Helson sets
We construct the following: a perfect non Dirichlet set every proper closed subset of which is Kronecker, A weak Kronecker set which is not an set; an independent countable Dirichlet set which is not Kronecker; a collection of -disjoint Kronecker sets whose union is independent but Helson ; A countable collection of disjoint Kronecker sets whose union is closed and independent but not Helson: a perfect independent Dirichlet set which is not Helson.
Some special W-almost periodic sets on the integers.
Some translation-invariant Banach function spaces which contain c₀
We produce several situations where some natural subspaces of classical Banach spaces of functions over a compact abelian group contain the space c₀.
Strict-2-associatedness for thin sets
Strong Riesz sets and polynomials
Sur les supports des transformées de Fourier-Stieltjes