Document Type

Article

Publication Date

2004

Abstract

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'.

Comments

First published in Proceedings of the American Mathematical Society 132.7 (2004), published by the American Mathematical Society.

DOI

10.1090/S0002-9939-04-07403-9