• Journal of the Korean Mathematical Society
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• v.59 no.2
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• pp.367-377
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• 2022

Let G be a non-discrete locally compact abelian group, and 𝜇 be a transformable and translation bounded Radon measure on G. In this paper, we construct a Segal algebra S_𝜇(G) in L¹(G) such that the generalized Poisson summation formula for 𝜇 holds for all f ∈ S_𝜇(G), for all x ∈ G. For the definitions of transformable and translation bounded Radon measures and the generalized Poisson summation formula, we refer to L. Argabright and J. Gil de Lamadrid's monograph in 1974.

• Journal of the Korean Statistical Society
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• v.29 no.3
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• pp.315-318
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• 2000

In this note we use the Poisson Summation Formula to generalize a result of Harris and Park (1994) on lattice distributions induced by uniform (0,1) random variables to those generated by random variables with step functions as their probability functions.

• Journal of the Korean Statistical Society
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• v.32 no.1
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• pp.21-24
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• 2003

In the recent papers by Harris and Park (1994) and by Hui and Park (2000), a family of lattice distributions derived from a sum of independent identically distributed random variables is examined. In this paper we generalize a result of Hui and Park (2000) on lattice distributions on the torus using the Poisson summation formula.