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 L 2 ( R ) , where each channeled signal is assigned a uniform but distinct sampling rate. We use Fourier duality between V ( ϕ ) and L 2 [ 0 , 2 π ] to find conditions under which there is a stable asymmetric multi-channel sampling formula on V ( ϕ ) .