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

• Autores: Colin C. Graham, Kathryn E. Hare
• Localización: Studia mathematica, ISSN 0039-3223, Vol. 177, Nº 1, 2006, págs. 9-24
• Idioma: inglés
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• Resumen

  • 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 "-Kronecker sets are FZI0 (with that stronger interpolation property).