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Advances in Fixed Point Theory ISSN 1927-6303 (Print)

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Adv. Fixed Point Theory 12 (2022), Article ID 12

Dynamical sampling in â„“2(Z)(d) and vector shift-invariant spaces

Zhenli Guo, Yue Su

PDF (166.1 KB) https://doi.org/10.28919/afpt/7715

Abstract

Dynamical sampling problem in which we seek to reconstruct a sequence or function in evolutionary systems via spatiotemporal trade-off. In this paper, we present the problem of dynamical sampling in ℓ2(Z)(d) and vector shift-invariant spaces. We first give a sufficient and necessary condition under which c∈ℓ2(Zd)(d) can be recovered by its spatial and temporal samples. Then to illustrate our main result, we give two examples to show that the sufficient and necessary condition in the main result is feasible. Finally, we study the dynamical sampling problem in vector shift-invariant spaces.

Published
2 November 2022
Volume
12 (2022)
License
CC BY 3.0

Copyright © 2022 Zhenli Guo, Yue Su. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Cite this article

Z. Guo, Y. Su, Dynamical sampling in â„“2(Z)(d) and vector shift-invariant spaces, Adv. Fixed Point Theory 12 (2022), 12. https://doi.org/10.28919/afpt/7715

BibTeX
@article{Guo2022,
  author  = {Guo, Zhenli and Su, Yue},
  title   = {Dynamical sampling in â„“2(Z)(d) and vector shift-invariant spaces},
  journal = {Adv. Fixed Point Theory},
  volume  = {12},
  year    = {2022},
  pages   = {12},
  doi     = {10.28919/afpt/7715}
}