  In this paper a sampling theory for unitary invariant subspaces associated to
locally compact abelian (LCA) groups is deduced. Working in the LCA group
context allows to obtain, in a unified way, sampling results valid for a wide
range of problems which are interesting in practice, avoiding also cumbersome
notation. Along with LCA groups theory, the involved mathematical technique is
that of frame theory which meets matrix analysis when appropriate dual frames
are computed.
