Multivariate vector sampling expansion in shift-invariant subspaces

Sampling theorems on a shift-invariant subspace are having a significant impact, since they avoid most of the problems associated with classical Shannon's theory. Vector sampling theorems on a shift-invariant subspace which are motivated by applications in multi-channel deconvolution and multi-source separation are active field of study. In this paper, we consider vector sampling theorems on a multivariate vector shift-invariant subspace. We give a multivariate vector sampling expansion on a multivariate vector shift-invariant subspace. Some equivalence conditions for the multivariate vector sampling expansion to hold are given. We also give several examples to illustrate the main result.