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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Convolution sampling and reconstruction of signals in a reproducing kernel subspace


Authors: M. Zuhair Nashed, Qiyu Sun and Jun Xian
Journal: Proc. Amer. Math. Soc. 141 (2013), 1995-2007
MSC (2010): Primary 42C15, 41A15, 46A35, 94A12
Published electronically: December 17, 2012
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Abstract: We consider convolution sampling and reconstruction of signals in certain reproducing kernel subspaces of $ L^p, 1\le p\le \infty $. We show that signals in those subspaces could be stably reconstructed from their convolution samples taken on a relatively separated set with small gap. Exponential convergence and error estimates are established for the iterative approximation-projection reconstruction algorithm.


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Additional Information

M. Zuhair Nashed
Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816
Email: zuhair.nashed@ucf.edu

Qiyu Sun
Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816
Email: qiyu.sun@ucf.edu

Jun Xian
Affiliation: Guangdong Province Key Laboratory of Computational Science and Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, People’s Republic of China
Email: xianjun@mail.sysu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11644-2
PII: S 0002-9939(2012)11644-2
Keywords: Convolution sampling, reproducing kernel subspace, iterative algorithm, error estimate
Received by editor(s): September 18, 2011
Published electronically: December 17, 2012
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2012 American Mathematical Society