Dynamical sampling in multiply generated shift-invariant spaces

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.

Keywords:

• Distributed sampling
• shift-invariant spaces
• Poisson summation formula
• Riesz basis

AMS Subject Classifications:

• 94A20
• 94A12
• 42C15
• 41A58

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Erratum

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)

Additional information

Funding

This work was supported partially by the National Natural Science Foundation of China [grant number 11326094], [grant number 11201336], [grant number 11401435], [grant number 11526150], [grant number 11371200].