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Sets of zero discrete harmonic density

Published online by Cambridge University Press:  20 November 2009

COLIN C. GRAHAM  and
KATHRYN E. HARE
COLIN C. GRAHAM
Affiliation:
Department of Mathematics, University of British Columbia, V6T 1Y4 Vancouver, B.C., Canada. e-mail: [email protected]
KATHRYN E. HARE
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1 Canada. e-mail: [email protected]
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Abstract

Let G be a compact, connected, abelian group with dual group Γ. The set E ⊂ has zero discrete harmonic density (z.d.h.d.) if for every open U ⊂ G and μ ∈ Md(G) there exists ν ∈ Md(U) with = on E. I0 sets in the duals of these groups have z.d.h.d. We give properties of such sets, exhibit non-Sidon sets having z.d.h.d., and prove union theorems. In particular, we prove that unions of I0 sets have z.d.h.d. and provide a new approach to two long-standing problems involving Sidon sets.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 148 , Issue 2 , March 2010 , pp. 253 - 266
Copyright
Copyright © Cambridge Philosophical Society 2009

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