J. Korean Math. Soc. 2022; 59(2): 367-377
Online first article February 11, 2022 Printed March 1, 2022
https://doi.org/10.4134/JKMS.j210290
Copyright © The Korean Mathematical Society.
Jyunji Inoue, Sin-Ei Takahasi
Hokkaido University; Laboratory of Mathematics and Games
Let $G$ be a non-discrete locally compact abelian group, and $\mu$ be a transformable and translation bounded Radon measure on $G$. In this paper, we construct a Segal algebra $S_{\mu}(G)$ in $L^1(G)$ such that the generalized Poisson summation formula for $\mu$ holds for all $f\in S_{\mu}(G)$, for all $x\in G$. 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.
Keywords: Locally compact abelian group, group algebra, Segal algebra, Radon measure, transformable measure, translation bounded measure, shift-bounded measure, Fourier transform, Poisson summation formula, generalized Poisson summation formula
MSC numbers: Primary 43A20; Secondary 42A38, 43A25
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