#### Document Type

Article

#### Publication Date

2004

#### Abstract

Suppose that Λ = (*a*Z + *b*) ∪ (*c*Z + *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 e_{λ}(*x*) = *e ^{i2πλx}*, λ is an element of Λ, form an orthogonal basis for some bounded measurable set Ω'.

#### Repository Citation

Pedersen, S.
(2004). The Dual Spectral Set Conjecture. *Proceedings of the American Mathematical Society, 132* (7), 2095-2101.

https://corescholar.libraries.wright.edu/math/6

#### DOI

10.1090/S0002-9939-04-07403-9

## Comments

First published in

Proceedings of the American Mathematical Society132.7 (2004), published by the American Mathematical Society.