Dynamical sampling in multiply generated shift-invariant spaces. Issue 5 (4th April 2017)

• Record Type: Journal Article
• Authors: Zhang, Qingyue; Liu, Bei; Li, Rui
• Is Part Of: Applicable analysis. Volume 96:Issue 5(2017)
• Page Start: 760
• Page End: 770
• Publication Date: 2017-04-04
• Subjects: Distributed sampling -- shift-invariant spaces -- Poisson summation formula -- Riesz basis; 94A20 -- 94A12 -- 42C15 -- 41A58; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1157586
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we study the problem of dynamical sampling in multiply generated shift-invariant spaces. We give a necessary and sufficient condition for stable reconstruction of signals in multiply generated shift-invariant spaces. Moreover, we show the condition which can make the dynamic sampling problem in multiply generated shift-invariant spaces into the dynamic sampling problem in . At last, we give a concrete example to show how to transform the dynamic sampling problem in shift-invariant space into the dynamic sampling problem in Our results generalize similar ones for the principal shift-invariant spaces.