Atomic decomposition via projective group representations

In the last few years, representations of functions (or distributions) as sums of ''building blocks'' have attracted much attention, e.g., time-frequency analysis and wavelet analysis. From a more abstract point of view, the Feichtinger/Grochenig theory discuss the same problem, with an integrable group representation as the starting point. Here we present a survey of the FG-theory combined with a generalization to projective representations; this makes it directly applicable to Gabor analysis. Furthermore we point out the connections to the existing theory for frame decomposition.