Multivariate Dynamical Sampling in ℓ2(ℤd) and Shift-Invariant Spaces

Abstract

In this article, we mainly study the multivariate dynamical sampling in ${\ell }^2\left({\mathbb{Z}}^d\right)$ and shift-invariant spaces. We first provide a sufficient and necessary condition for $c\in {\ell }^2\left({\mathbb{Z}}^d\right)$ which can be reconstructed by its spatial and temporal samples. Then we give a concrete example to show that the sufficient and necessary condition is feasible. Finally, we discuss the multivariate dynamical sampling problem in shift-invariant spaces.

Keywords:

• Dynamical sampling
• multivariate dynamical sampling
• shift-invariant spaces

2000 MATHEMATICS Subject Classification:

• 94A20
• 94A12
• 42C15
• 41A58

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported partially by the National Natural Science Foundation of China (11326094, 11401435 and 11601384) and the Natural Science Research Project of Higher Education of Tianjin (2018KJ147, 2018KJ148).