Dynamical sampling in multiply generated shift-invariant spaces

作者：Zhang, Qingyue; Liu, Bei^*; Li, Rui

来源：APPLICABLE ANALYSIS, 2017, 96(5): 760-770.

DOI：10.1080/00036811.2016.1157586

• Distributed sampling
• shift-invariant spaces
• Poisson summation formula
• Riesz basis
• 94A20
• 94A12
• 42C15
• 41A58

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 shiftinvariant 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 l2(Z). At last, we give a concrete example to show how to transform the dynamic sampling problem in shiftinvariant space into the dynamic sampling problem in l2(Z). Our results generalize similar ones for the principal shift-invariant spaces.

• 出版日期2017
• 单位天津理工大学