Authors: Qingyue Zhang
Addresses: College of Science, Tianjin University of Technology, Tianjin 300384, China
Abstract: 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.
Keywords: sampling theorems; vector sampling theorems; shift-invariant subspaces; super Hilbert space; frames.
International Journal of Dynamical Systems and Differential Equations, 2020 Vol.10 No.1, pp.19 - 33
Received: 21 Feb 2018
Accepted: 24 May 2018
Published online: 06 Feb 2020 *