ε-Kronecker and I₀sets in abelian groups, III: interpolation by measures on small sets

Abstract

Let $U$ be an open subset of a locally compact abelian group $G$ and let $E$ be a subset of its dual group ${\mit\Gamma} $. We say $E$ is $I_0(U)$ if every bounded sequence indexed by $E$ can be interpolated by the Fourier transform of a discrete measure