English

Multivariate Dynamical Sampling in $l^2(\mathbb{Z}^2)$ and Shift-Invariant Spaces Associated with Linear Canonical Transform

Functional Analysis 2021-10-28 v1

Abstract

In this paper, we investigate the multivariate dynamical sampling problem in l2(Z2)l^2(\mathbb{Z}^2) associated with the two-dimensional discrete time non-separable linear canonical transform (2D-DT-NS-LCT) and shift-invariant spaces associated with the two-dimensional non-separable linear canonical transform (2D-NS-LCT), respectively. Specifically, we derive a sufficient and necessary condition under which a sequence in l2(Z2)l^2(\mathbb{Z}^2) (or a function in a shift-invariant space) can be stably recovered from its dynamical sampling measurements associated with the 2D-DT-NS-LCT (or the 2D-NS-LCT). We also present a simple example to elucidate our main results.

Cite

@article{arxiv.2110.14167,
  title  = {Multivariate Dynamical Sampling in $l^2(\mathbb{Z}^2)$ and Shift-Invariant Spaces Associated with Linear Canonical Transform},
  author = {Haiye Huo and Li Xiao},
  journal= {arXiv preprint arXiv:2110.14167},
  year   = {2021}
}
R2 v1 2026-06-24T07:13:17.709Z