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

• Autorzy: Colin C. Graham , Kathryn E. Hare
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 42A55: Lacunary series of trigonometric and other functions; Riesz products
• 43A05: Measures on groups and semigroups, etc.
• 42A82: Positive definite functions
• 43A25: Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
• 43A46: Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 177
• Numer: 1
• Strony: 9-24

Daty

wydano

2006

Twórcy

autor

Colin C. Graham

• Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada
• RR#1-D-156, Bowen Island, B.C., Canada V0N 1G0

autor

Kathryn E. Hare

• Department of Pure Mathematics, University of Waterloo, Waterloo, Ont., Canada N2L 3G1

Identyfikatory

DOI

10.4064/sm177-1-2