Multi-tiling and Riesz bases

Sigrid Grepstad, Nir Lev

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


Let S be a bounded, Riemann measurable set in Rd, and Λ be a lattice. By a theorem of Fuglede, if S tiles Rd with translation set Λ, then S has an orthogonal basis of exponentials. We show that, under the more general condition that S multi-tiles Rd with translation set Λ, S has a Riesz basis of exponentials. The proof is based on Meyer's quasicrystals.

Original languageEnglish
Pages (from-to)1-6
Number of pages6
JournalAdvances in Mathematics
StatePublished - 15 Feb 2014


  • Quasicrystals
  • Riesz bases
  • Tiling


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