ABSTRACT
The basic theory of frames is reviewed, and special topics dealing with Gabor frames and decompositions are developed. These topics include Gabor decompositions of L 1 and of Bessel potential spaces. (Sobolev spaces are Bessel potential spaces.) Frames of translates in L 2 are characterized; and the Balian-Low theorem for L 2 is proved. The former result is not only useful for the Gabor theory, but is the basis of multiresolution analysis frames; the latter result is related to the classical uncertainty principle inequality.
