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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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Exact iterative reconstruction algorithm for multivariate irregularly sampled functions in spline-like spaces: The $L^p$-theory
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by Akram Aldroubi and Hans Feichtinger PDF
Proc. Amer. Math. Soc. 126 (1998), 2677-2686 Request permission

Abstract:

We prove that the exact reconstruction of a function $s$ from its samples $s (x_i)$ on any “sufficiently dense" sampling set $\{x_i\}_{i\in \Lambda }$ can be obtained, as long as $s$ is known to belong to a large class of spline-like spaces in $L^p (\mathcal {R}^n)$. Moreover, the reconstruction can be implemented using fast algorithms. Since a limiting case is the space of bandlimited functions, our result generalizes the classical Shannon-Whittaker sampling theorem on regular sampling and the Paley-Wiener theorem on non-uniform sampling.
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Additional Information
  • Akram Aldroubi
  • Affiliation: National Institutes of Health, Biomedical Engineering and Instrumentation Program, Bethesda, Maryland 20892
  • Address at time of publication: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
  • Email: aldroubi@helix.nih.gov, aldroubi@math.vanderbilt.edu
  • Hans Feichtinger
  • Affiliation: University of Vienna, Department of Mathematics, Strudlhofg. 4, A-1090 Wien, Austria
  • MR Author ID: 65680
  • ORCID: 0000-0002-9927-0742
  • Email: fei@tyche.mat.univie.ac.at
  • Received by editor(s): January 28, 1997
  • Additional Notes: This research was partially supported through the FWF-project S-7001-MAT of the Austrian Science Foundation.

  • Dedicated: Dedicated to the memory of Richard J. Duffin
  • Communicated by: Palle E. T. Jorgensen
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 2677-2686
  • MSC (1991): Primary 42C15, 46A35, 46E15, 46N99, 47B37
  • DOI: https://doi.org/10.1090/S0002-9939-98-04319-6
  • MathSciNet review: 1451788