Gabor Frames for Quasicrystals, $K$-theory, and Twisted Gap Labeling
Operator Algebras
2017-09-07 v1 Functional Analysis
K-Theory and Homology
Abstract
We study the connection between Gabor frames for quasicrystals, the topology of the hull of a quasicrystal and the -theory of the twisted groupoid -algebra arising from a quasicrystal. In particular, we construct a finitely generated projective module over related to time-frequency analysis, and any multiwindow Gabor frame for can be used to construct an idempotent in representing in We show for lattice subsets in dimension two, this element corresponds to the Bott element in allowing us to prove a twisted version of Bellissard's gap labeling theorem.
Cite
@article{arxiv.1411.7269,
title = {Gabor Frames for Quasicrystals, $K$-theory, and Twisted Gap Labeling},
author = {Michael Kreisel},
journal= {arXiv preprint arXiv:1411.7269},
year = {2017}
}