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Title: Multivariate vector sampling expansion in shift-invariant subspaces

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.

DOI: 10.1504/IJDSDE.2020.104900

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: 05 Feb 2020 *

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