ε-Kronecker and I₀ sets in abelian groups, IV: interpolation by non-negative measures

Colin C. Graham, and Kathryn E. Hare. "ε-Kronecker and I₀ sets in abelian groups, IV: interpolation by non-negative measures." Studia Mathematica 177.1 (2006): 9-24. <http://eudml.org/doc/284750>.

@article{ColinC2006,
abstract = { 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). },
author = {Colin C. Graham, Kathryn E. Hare},
journal = {Studia Mathematica},
keywords = {Fatou-Zygmund interpolation set; interpolation set; -Kronecker set; Hadamard set},
language = {eng},
number = {1},
pages = {9-24},
title = {ε-Kronecker and I₀ sets in abelian groups, IV: interpolation by non-negative measures},
url = {http://eudml.org/doc/284750},
volume = {177},
year = {2006},
}

TY - JOUR
AU - Colin C. Graham
AU - Kathryn E. Hare
TI - ε-Kronecker and I₀ sets in abelian groups, IV: interpolation by non-negative measures
JO - Studia Mathematica
PY - 2006
VL - 177
IS - 1
SP - 9
EP - 24
AB - 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).
LA - eng
KW - Fatou-Zygmund interpolation set; interpolation set; -Kronecker set; Hadamard set
UR - http://eudml.org/doc/284750
ER -