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The Dual Spectral Set Conjecture, Steen Pedersen
The Dual Spectral Set Conjecture, Steen Pedersen
Mathematics and Statistics Faculty Publications
Suppose that Λ = (aZ + b) ∪ (cZ + d) where a, b, c, d are real numbers such that a ≠ 0 and c ≠ 0. The union is not assumed to be disjoint. It is shown that the translates Ω + λ, λ is an element of Λ, tile the real line for some bounded measurable set Ω if and only if the exponentials eλ(x) = ei2πλx, λ is an element of Λ, form an orthogonal basis for some bounded measurable set Ω'.