• Title/Summary/Keyword: Poisson Summation Formula

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CONSTRUCTIONS OF SEGAL ALGEBRAS IN L1(G) OF LCA GROUPS G IN WHICH A GENERALIZED POISSON SUMMATION FORMULA HOLDS

  • Inoue, Jyunji;Takahasi, Sin-Ei
    • 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 S𝜇(G) in L1(G) such that the generalized Poisson summation formula for 𝜇 holds for all f ∈ S𝜇(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.

A Note on a Family of Lattice Distributions

  • Stefen Hui;Park, C. J.
    • 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.

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A NOTE ON LATTICE DISTRIBUTIONS ON THE TORUS

  • Park, Chong-Jin;Lee, Kyu-Seok
    • 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.