Multivariate Dynamical Sampling in ℓ2(ℤd) and Shift-Invariant Spaces. (26th April 2019)

• Record Type: Journal Article
• Authors: Zhang, Qingyue; Li, Zunxian
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 6(2019)
• Page Start: 670
• Page End: 684
• Publication Date: 2019-04-26
• Subjects: Dynamical sampling -- multivariate dynamical sampling -- shift-invariant spaces; 94A20 -- 94A12 -- 42C15 -- 41A58; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1561471
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this article, we mainly study the multivariate dynamical sampling inℓ 2 ( ℤ d ) and shift-invariant spaces. We first provide a sufficient and necessary condition forc ∈ ℓ 2 ( ℤ d ) 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.