Riesz bases of exponentials on multiband spectra

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Let S be the union of finitely many disjoint intervals on ℝ. Suppose that there are two real numbers α, β such that the length of each interval belongs to ℤα + ℤβ. We use quasicrystals to construct a discrete set Λ ⊂ ℝ such that the system of exponentials {exp 2πiλx, λ ∈ Λ} is a Riesz basis in the space L 2(S).

Original languageEnglish
Pages (from-to)3127-3132
Number of pages6
JournalProceedings of the American Mathematical Society
Issue number9
StatePublished - Sep 2012
Externally publishedYes


  • Multiband signals
  • Quasicrystals
  • Riesz bases


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