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.
Acknowledgements
The authors thank the editor and the referees very much for elaborate and valuable suggestions which helped to improve this paper.
Notes
No potential conflict of interest was reported by the authors.
This article was originally published with errors. This version has been corrected. Please see Erratum (http://dx.doi.org/10.1080/00036811.2016.1180789)