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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Convolution sampling and reconstruction of signals in a reproducing kernel subspace
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by M. Zuhair Nashed, Qiyu Sun and Jun Xian PDF
Proc. Amer. Math. Soc. 141 (2013), 1995-2007 Request permission

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
  • Received by editor(s): September 18, 2011
  • Published electronically: December 17, 2012
  • Communicated by: Michael T. Lacey
  • © Copyright 2012 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 1995-2007
  • MSC (2010): Primary 42C15, 41A15, 46A35, 94A12
  • DOI: https://doi.org/10.1090/S0002-9939-2012-11644-2
  • MathSciNet review: 3034426