Narrow Results

The theory of vector-valued frames (also called superframes) has important applications in signal multiplexing, and has interested many mathematicians in recent years. In this paper, we introduce the notion of weak Gabor duals of type II under the setting of subspaces $L^2(S,{ℂ}^L)$, where $S$ is a periodic subset of $ℝ$. Using the Zak transform matrix method, we characterize weak Gabor duals of type II and their uniqueness. An example is also presented to illustrate the generality of our results.