Journal
JOURNAL OF FUNCTIONAL ANALYSIS
Volume 270, Issue 3, Pages 1001-1030Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jfa.2015.11.011
Keywords
Quasicrystals; Gabor analysis; Gap labeling
Categories
Funding
- NSF [DMS-1206159]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1206159] Funding Source: National Science Foundation
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We study the connection between Gabor frames for quasicrystals, the topology of the hull of a quasicrystal A, and the K-theory of an associated twisted groupoid algebra. In particular, we construct a finitely generated projective module over this algebra, and any multiwindow Gabor frame for A can be used to construct an idempotent representing this module in K-theory. For lattice subsets in dimension two, this allows us to prove a twisted version of Bellissard's gap labeling theorem. (C) 2015 Elsevier Inc. All rights reserved.
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