Cut-and-project sets and their -duals
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 ϵ-dual. The ϵ-dual of a lattice is the reciprocal lattice, and that of a cut-and-projec...
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| Published in | Philosophical magazine (Abingdon, England) Vol. 87; no. 18-21; pp. 2847 - 2854 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Taylor & Francis
21.06.2007
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| Online Access | Get full text |
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| Summary: | 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 ϵ-dual. The ϵ-dual of a lattice is the reciprocal lattice, and that of a cut-and-project set is contained by the diffraction pattern. Let
be the cut-and-project set determined by locally compact Hausdorff Abelian groups
, lattice
and a window
. Then we prove
by using the Baake-Lenz-Schlottmann measure dynamical system of point sets. Moreover, we characterize the symmetries of
by the symmetries of W. |
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| Bibliography: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 SourceType-Scholarly Journals-2 ObjectType-Feature-2 ObjectType-Conference Paper-1 SourceType-Conference Papers & Proceedings-1 ObjectType-Article-3 |
| ISSN: | 1478-6435 1478-6443 |
| DOI: | 10.1080/14786430701373698 |