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Mathematics of Computation

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

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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A generalized sampling theorem for locally compact abelian groups
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by Adel Faridani PDF
Math. Comp. 63 (1994), 307-327 Request permission

Abstract:

We present a sampling theorem for locally compact abelian groups. The sampling sets are finite unions of cosets of a closed subgroup. This generalizes the well-known case of nonequidistant but periodic sampling on the real line. For nonbandlimited functions an ${L_1}$-type estimate for the aliasing error is given. We discuss the application of the theorem to a class of sampling sets in ${{\mathbf {R}}^s}$, give a general algorithm for a computer implementation, present a detailed description of the implementation for the s-dimensional torus group, and point out connections to lattice rules for numerical integration.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Math. Comp. 63 (1994), 307-327
  • MSC: Primary 43A25; Secondary 65Dxx, 65T20, 94A05
  • DOI: https://doi.org/10.1090/S0025-5718-1994-1240658-6
  • MathSciNet review: 1240658