Atomic decomposition via projective group representations

Abstract

In thelast few years, representations of funo tions (or distributions) as sums of “building blocks” have attracted much attention, e.g., time-frequencyanalysis andwavelet analysis. From a more abstract point of view, the Feichtinger/Gröchenig 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. © 1996 Rocky Mountain Mathematics Consortium.