Gabor Frames for Quasicrystals and K-theory
Gabor Frames for Quasicrystals and K-theory
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Date
2015
Authors
Kreisel, Michael Charles
Advisor
Rosenberg, Jonathan
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Abstract
We study the connection between Gabor frames for quasicrystals, the topology of the hull of a quasicrystal, and the K-theory of an associated twisted groupoid algebra. In particular, we construct a finitely generated projective module over this algebra, and multiwindow Gabor frames can be used to construct an idempotent representing the module in K-theory. For lattice subsets in dimension two, this allows us to prove a twisted version of Bellissard's gap labeling theorem. By viewing Gabor frames in this operator algebraic framework, we are also able to show that for certain quasicrystals it is not possible to construct a tight multiwindow Gabor frame.