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

Colin C. Graham; Kathryn E. Hare

Studia Mathematica (2006)

- Volume: 177, Issue: 1, page 9-24
- ISSN: 0039-3223

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topColin 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 -

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