ε-Kronecker and I₀ sets in abelian groups, III: interpolation by measures on small sets

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

Abstrakty

EN

Let U be an open subset of a locally compact abelian group G and let E be a subset of its dual group Γ. We say E is I₀(U) if every bounded sequence indexed by E can be interpolated by the Fourier transform of a discrete measure supported on U. We show that if E·Δ is I₀ for all finite subsets Δ of a torsion-free Γ, then for each open U ⊂ G there exists a finite set F ⊂ E such that E∖F is I₀(U). When G is connected, F can be taken to be empty. We obtain a much stronger form of that for Hadamard sets and ε-Kronecker sets, and a slightly weaker general form when Γ has torsion. This extends previously known results for Sidon, ε-Kronecker, and Hadamard sets.

Kategorie tematyczne

• 42A55: Lacunary series of trigonometric and other functions; Riesz products
• 43A05: Measures on groups and semigroups, etc.
• 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: 2005
• Tom: 171
• Numer: 1
• Strony: 15-32

Daty

wydano

2005

Twórcy

autor

Colin C. Graham

• University of British Columbia

autor

Kathryn E. Hare

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

Identyfikatory

DOI

10.4064/sm171-1-2