Let a, b, c > 0. We investigate the characterization problem which asks for a classification of all the triples (a, b, c) such that the Weyl-Heisenberg system
$$\left\{ {{e^{2\pi imbx}} \times {\chi _{[na,na + c)}}:m,n \in {\Bbb Z}} \right\}$$
is a frame for L
2(ℝ). It turns out that the answer to the problem is quite complicated, see Gu and Han (2008) and Janssen (2003). Using a dilation technique, one can reduce the problem to the case where b = 1 and only let a and c vary. In this paper, we extend the Zak transform technique and u...
