Gabor Frames for Quasicrystals and K-theory

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.