$\varepsilon $-Kronecker and $I_{0}$ sets in abelian groups, IV: interpolation by non-negative measures

Tom 177 / 2006

Colin C. Graham, Kathryn E. Hare Studia Mathematica 177 (2006), 9-24 MSC: Primary 42A55, 43A46; Secondary 43A05, 43A25, 42A82. DOI: 10.4064/sm177-1-2

Streszczenie

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).

Autorzy

  • Colin C. GrahamDepartment of Mathematics
    University of British Columbia
    Vancouver, B.C., Canada
    and
    RR#1–D-156
    Bowen Island, B.C., Canada V0N 1G0
    e-mail
  • Kathryn E. HareDepartment of Pure Mathematics
    University of Waterloo
    Waterloo, Ont., Canada N2L 3G1
    e-mail

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