## A generalized sampling theorem for locally compact abelian groups

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- 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