Sampling and Average Sampling in Quasi Shift-Invariant Spaces. (26th July 2020)

• Record Type: Journal Article
• Authors: Kumar, Anuj; Sampath, Sivananthan
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 10(2020)
• Page Start: 1246
• Page End: 1271
• Publication Date: 2020-07-26
• Subjects: Bernstein inequality -- frames and quasi nonuniform sampling -- reproducing kernel Hilbert spaces -- Riesz basis -- shift-invariant spacesshift-invariant spaces; 94A20 -- 42C15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1748054
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we study the sampling and average sampling problem in a quasi shift-invariant space V X ( φ ), where X is a discrete subset of R and φ is a continuously differentiable positive definite function satisfying certain decay conditions. We show that any f belonging to V X ( φ ) can be uniquely and stably reconstructed from its samples { f ( y k ) : k ∈ Z } as well as from its average samples provided sampling points { y k : k ∈ Z } are close enough. Further, iterative reconstruction algorithms for reconstruction of a function f belonging to V X ( φ ) from its samples { f ( y k ) : k ∈ Z } as well as from its average samples are also provided.