|Dept.||Norwegian University of Science and Technology|
The talk discusses the structure of Heisenberg modules over noncommutative tori and their description in terms of standard module frames. We relate these module frames to Gabor frames that are used in signal analysis. There is a dictionary between noncommutative tori and Gabor frames, for example the construction of projections in noncommutative tori is equivalent to the construction of a Gabor frame.
We also characterize standard module frames of a Heisenberg module in terms of Riesz basic sequences and superframes which extend duality results on Gabor frames. Applications to sigma moudels over noncommutative tori are briefly discussed as well. The talk is partially based on joint work with L. Dabrowski, M. S.Jakobsen and G. Landi.