Dissertation/Thesis Abstract

Gabor frames for quasicrystals and K-theory
by Kreisel, Michael, Ph.D., University of Maryland, College Park, 2015, 95; 3711683
Abstract (Summary)

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.

Indexing (document details)
Advisor: Rosenberg, Jonathan
Commitee: Balan, Radu, Czaja, Wojciech, Okoudjou, Kasso, Yakovenko, Victor
School: University of Maryland, College Park
Department: Mathematics
School Location: United States -- Maryland
Source: DAI-B 76/11(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Gabor frames, K-theory, Operator algebras, Quasicrystals
Publication Number: 3711683
ISBN: 978-1-321-88031-1
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