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).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm177-1-2,
author = {Colin C. Graham and Kathryn E. Hare},
title = {e-Kronecker and I0 sets in abelian groups, IV: interpolation by non-negative measures},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {9-24},
zbl = {1138.43006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm177-1-2}
}
Colin C. Graham; Kathryn E. Hare. ε-Kronecker and I₀ sets in abelian groups, IV: interpolation by non-negative measures. Studia Mathematica, Tome 173 (2006) pp. 9-24. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm177-1-2/