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- W1912458701 abstract "We study the connection between Gabor frames for quasicrystals, the topology of the hull of a quasicrystal $Lambda,$ and the $K$-theory of the twisted groupoid $C^*$-algebra $mathcal{A}_sigma$ arising from a quasicrystal. In particular, we construct a finitely generated projective module $mathcal{H}_L$ over $mathcal{A}_sigma$ related to time-frequency analysis, and any multiwindow Gabor frame for $Lambda$ can be used to construct an idempotent in $M_N(mathcal{A}_sigma)$ representing $mathcal{H}_L$ in $K_0(mathcal{A}_sigma).$ We show for lattice subsets in dimension two, this element corresponds to the Bott element in $K_0(mathcal{A}_sigma),$ allowing us to prove a twisted version of Bellissard's gap labeling theorem." @default.
- W1912458701 created "2016-06-24" @default.
- W1912458701 creator A5075152591 @default.
- W1912458701 date "2014-11-26" @default.
- W1912458701 modified "2023-09-27" @default.
- W1912458701 title "Gabor Frames for Quasicrystals, $K$-theory, and Twisted Gap Labeling" @default.
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