Shift-modulation invariant spaces on LCA groups

A (K, A) shift-modulation invariant space is a subspace of L-2 (G) that is invariant under translations along elements in K and modulations by elements in A. Here G is a locally compact abelian group, and K and Lambda are closed subgroups of G and the dual group (G) over cap, respectively. We provide a characterization of shift-modulation invariant spaces when K and Lambda are uniform lattices. This extends previous results known for L-2 (R-d). We develop fiberization techniques and suitable range functions adapted to LCA groups needed to provide the desired characterization.