dc.contributor.advisor Luef, Franz dc.contributor.author Enstad, Ulrik Bo Rufus dc.date.accessioned 2016-06-27T14:00:44Z dc.date.available 2016-06-27T14:00:44Z dc.date.created 2016-06-01 dc.date.issued 2016 dc.identifier ntnudaim:13009 dc.identifier.uri http://hdl.handle.net/11250/2394273 dc.description.abstract A link between noncommutative geometry and time-frequency analysis is used to show that the TKNN equation violates existence results for Gabor frames with atoms in the Schwartz space. In particular, we use that the Schwartz space is an equivalence bimodule between smooth noncommutative tori associated to $\theta$ and $-1/\theta$. As a consequence, projections in smooth noncommutative tori correspond to tight Gabor frames generated by Schwartz functions. We calculate the trace and the Connes-Chern number of these projections and show that these provide counterexamples to the TKNN equation for rational smooth noncommutative tori. dc.language eng dc.publisher NTNU dc.subject Matematikk (for international students), - dc.title Rational Noncommutative Tori and Gabor Frames dc.type Master thesis dc.source.pagenumber 94
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