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

Colin C. Graham; Kathryn E. Hare

Studia Mathematica (2005)

- Volume: 171, Issue: 1, page 15-32
- ISSN: 0039-3223

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topColin 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 -

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