Asymmetric multi-channel sampling in shift invariant spaces

We develop an asymmetric multi-channel sampling on a shift invariant space V(ϕ) with a Riesz generator ϕ(t) in L2(R), where each channeled signal is assigned a uniform but distinct sampling rate. We use Fourier duality between V(ϕ) and L2[0,2π] to find conditions under which there is a stable asymmetric multi-channel sampling formula on V(ϕ).