TY - JOUR
T1 - Multi-tiling and Riesz bases
AU - Grepstad, Sigrid
AU - Lev, Nir
PY - 2014/2/15
Y1 - 2014/2/15
N2 - 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.
AB - 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.
KW - Quasicrystals
KW - Riesz bases
KW - Tiling
UR - http://www.scopus.com/inward/record.url?scp=84887566722&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2013.10.019
DO - 10.1016/j.aim.2013.10.019
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AN - SCOPUS:84887566722
SN - 0001-8708
VL - 252
SP - 1
EP - 6
JO - Advances in Mathematics
JF - Advances in Mathematics
ER -