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

Colin C. Graham, and Kathryn E. Hare. "ε-Kronecker and I₀ sets in abelian groups, III: interpolation by measures on small sets." Studia Mathematica 171.1 (2005): 15-32. <http://eudml.org/doc/285258>.

@article{ColinC2005,
abstract = {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.},
author = {Colin C. Graham, Kathryn E. Hare},
journal = {Studia Mathematica},
keywords = {Kronecker sets; Hadamard sequences; sets; Bohr group},
language = {eng},
number = {1},
pages = {15-32},
title = {ε-Kronecker and I₀ sets in abelian groups, III: interpolation by measures on small sets},
url = {http://eudml.org/doc/285258},
volume = {171},
year = {2005},
}

TY - JOUR
AU - Colin C. Graham
AU - Kathryn E. Hare
TI - ε-Kronecker and I₀ sets in abelian groups, III: interpolation by measures on small sets
JO - Studia Mathematica
PY - 2005
VL - 171
IS - 1
SP - 15
EP - 32
AB - 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.
LA - eng
KW - Kronecker sets; Hadamard sequences; sets; Bohr group
UR - http://eudml.org/doc/285258
ER -