Tigth Gabor frames and projections in noncommutative tori
given at strobl09 (18.06.09 16:45)
Our approach to the construction of projective modules over noncommutative tori in terms of Gabor analysis allows us to link Rieffel's projections in noncommutative tori with the construction of Gabor frames. The
main result demonstrates that Rieffel's condition on the existence of projections in noncommutative tori is equivalent to the Wexler-Raz biorthogonality relations for tight Gabor frames. Therefore we are able to apply results on the existence of Gabor frames to construct projections in noncommutative tori. The projection associated with a Gabor frame generated by a Gaussian turns out to be Boca's projection and the result of Lyubarski and Seip allows us to characterize the range of existence of Boca's projection.