Geodesic
$\varepsilon $-Kronecker and $I_{0}$ sets in abelian groups, IV: interpolation by non-negative measures
Colin C. Graham1 ; Kathryn E. Hare2
1Department of Mathematics University of British Columbia Vancouver, B.C., Canada and RR#1–D-156 Bowen Island, B.C., Canada V0N 1G0
2Department of Pure Mathematics University of Waterloo Waterloo, Ont., Canada N2L 3G1
Studia Mathematica, Tome 177 (2006) no. 1, pp. 9-24
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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A subset $E$ of a discrete abelian group is a “Fatou–Zygmund interpolation set” ($F\kern-.75pt ZI_0$ 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 $F\kern-.75pt ZI_0$ set of the same cardinality (if the group is torsion free, a stronger interpolation property holds) and that $\varepsilon $-Kronecker sets are $F\kern-.75pt ZI_0$ (with that stronger interpolation property).
DOI : 10.4064/sm177-1-2
Keywords: subset discrete abelian group fatou zygmund interpolation set kern set every bounded hermitian function restriction fourier stieltjes transform discrete non negative measure every infinite subset discrete abelian group contains kern set cardinality group torsion stronger interpolation property holds varepsilon kronecker sets kern stronger interpolation property

Colin C. Graham  1   ; Kathryn E. Hare  2

1 Department of Mathematics University of British Columbia Vancouver, B.C., Canada and RR#1–D-156 Bowen Island, B.C., Canada V0N 1G0
2 Department of Pure Mathematics University of Waterloo Waterloo, Ont., Canada N2L 3G1 
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 interpolation by non-negative measures
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Colin C. Graham; Kathryn E. Hare. $\varepsilon $-Kronecker and $I_{0}$ sets in abelian groups, IV:
 interpolation by non-negative measures. Studia Mathematica, Tome 177 (2006) no. 1, pp. 9-24. doi: 10.4064/sm177-1-2

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