A GENERALIZED SAMPLING THEOREM FOR LOCALLY COMPACT ABELIAN-GROUPS

We present a sampling theorem for locally compact abelian groups. The sampling sets are finite unions of cosets of a closed subgroup. This g eneralizes the well-known case of nonequidistant but periodic sampling on the real line. For nonbandlimited functions an L1-type estimate fo r the aliasing error is given. We discuss the application of the theor em to a class of sample sets in R(s), give a general algorithm for a c omputer implementation, present a detailed description of the implemen tation for the s-dimensional torus group, and point out connections to lattice rules for numerical integration.