TY - JOUR
T1 - Cut-and-project sets and their ε-duals
AU - Akama, Y.
AU - Iizuka, S.
N1 - Funding Information:
The second author is supported by COE ‘Exploring New Science by Bridging Particle–Matter Hierarchy,’ Graduate School of Science, Tohoku University.
PY - 2007/7
Y1 - 2007/7
N2 - Motivated by approximation and real analysis, Meyer introduced model sets (also called cut-and-project sets), which are used as mathematical models of quasicrystals. In his study, a central role was played by the -dual. The -dual of a lattice is the reciprocal lattice, and that of a cut-and-project set is contained by the diffraction pattern. Let [image omitted] be the cut-and-project set determined by locally compact Hausdorff Abelian groups [image omitted], lattice [image omitted] and a window [image omitted]. Then we prove [image omitted] by using the Baake-Lenz-Schlottmann measure dynamical system of point sets. Moreover, we characterize the symmetries of [image omitted] by the symmetries of W.
AB - Motivated by approximation and real analysis, Meyer introduced model sets (also called cut-and-project sets), which are used as mathematical models of quasicrystals. In his study, a central role was played by the -dual. The -dual of a lattice is the reciprocal lattice, and that of a cut-and-project set is contained by the diffraction pattern. Let [image omitted] be the cut-and-project set determined by locally compact Hausdorff Abelian groups [image omitted], lattice [image omitted] and a window [image omitted]. Then we prove [image omitted] by using the Baake-Lenz-Schlottmann measure dynamical system of point sets. Moreover, we characterize the symmetries of [image omitted] by the symmetries of W.
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U2 - 10.1080/14786430701373698
DO - 10.1080/14786430701373698
M3 - Article
AN - SCOPUS:34547351698
VL - 87
SP - 2847
EP - 2854
JO - Philosophical Magazine
JF - Philosophical Magazine
SN - 1478-6435
IS - 18-21
ER -