A Uniform Boundedness Principle for Compact Sets and the Decay of Fourier Transforms.
Erratum to the Paper: A Uniform Boundedness Principle for Compact Sets and the Decay of Fourier Transforms.
The Algebraic Radical of a Normed Ideal in L1 (G).
Non-Sidon sets in the support of a Fourier-Stieltjes transform
Associate and pseudoassociate sets in LCA groups, II
Associate and pseudoassociate sets in LCA groups
The Gelfand transforms of a convolution measure algebra
Two remarks on the Fourier-Stieltjes transforms of continuous measures
Three results on I-sets
Sets of interpolation for Fourier transforms of bimeasures
Existence of large ε-Kronecker and FZI₀(U) sets in discrete abelian groups
Let G be a compact abelian group with dual group Γ and let ε > 0. A set E ⊂ Γ is a “weak ε-Kronecker set” if for every φ:E → there exists x in the dual of Γ such that |φ(γ)- γ(x)| ≤ ε for all γ ∈ E. When ε < √2, every bounded function on E is known to be the restriction of a Fourier-Stieltjes transform of a discrete measure. (Such sets are called I₀.) We show that for every infinite set E there exists a weak 1-Kronecker subset F, of the same cardinality as E, provided there are not “too many”...
Characterizing Sidon sets by interpolation properties of subsets
Pisier's characterization of Sidon sets as containing proportional-sized quasi-independent subsets is given a sharper form for groups with only a finite number of elements having orders a power of 2. No such improvement is possible for a general Sidon subset of a group having an infinite number of elements of order 2. The method used also gives several sharper forms of Ramsey's characterization of Sidon sets as containing proportional-sized I₀-subsets in a uniform way, again in groups containing...
ε-Kronecker and I₀ sets in abelian groups, III: interpolation by measures on small sets
Let U be an open subset of a locally compact abelian group G and let E be a subset of its dual group Γ. We say E is I₀(U) if every bounded sequence indexed by E can be interpolated by the Fourier transform of a discrete measure supported on U. We show that if E·Δ is I₀ for all finite subsets Δ of a torsion-free Γ, then for each open U ⊂ G there exists a finite set F ⊂ E such that E∖F is I₀(U). When G is connected, F can be taken to be empty. We obtain a much stronger form of that for Hadamard sets...
ε-Kronecker and I₀ sets in abelian groups, IV: interpolation by non-negative measures
A subset E of a discrete abelian group is a "Fatou-Zygmund interpolation set" (FZI₀ set) if every bounded Hermitian function on E is the restriction of the Fourier-Stieltjes transform of a discrete, non-negative measure. We show that every infinite subset of a discrete abelian group contains an FZI₀ set of the same cardinality (if the group is torsion free, a stronger interpolation property holds) and that ε-Kronecker sets are FZI₀ (with that stronger interpolation property). ...
Separable translation-invariant subspaces of M(G) and other dual spaces on locally compact groups
Sur les supports des transformées de Fourier-Stieltjes
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