Riesz bases of exponentials on multiband spectra

Let $S$ be the union of finitely many disjoint intervals on the real line. Suppose that there are two real numbers $α, β$ such that the length of each interval belongs to $Z α+ Z β$. We use quasicrystals to construct a discrete set of real frequencies such that the corresponding system of exponentials is a Riesz basis in the space $L^2(S)$.

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