대한수학회지 (Journal of the Korean Mathematical Society)

  • 제59권2호
  • /
  • Pages.367-377
  • /
  • 2022
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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CONSTRUCTIONS OF SEGAL ALGEBRAS IN L1(G) OF LCA GROUPS G IN WHICH A GENERALIZED POISSON SUMMATION FORMULA HOLDS

  • 투고 : 2021.05.05
  • 심사 : 2021.12.10
  • 발행 : 2022.03.01
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초록

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.

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과제정보

Authors express deep thanks to a reviewer of the paper. With his suitable comments, queries and advices, the paper has drastically improved and becomes shorter.

참고문헌

  1. L. Argabright and J. Gil de Lamadrid, Fourier analysis of unbounded measures on locally compact abelian groups, Memoirs of the American Mathematical Society, No. 145, American Mathematical Society, Providence, RI, 1974.
  2. C. Berg and G. Forst, Potential theory on locally compact abelian groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 87, Springer-Verlag, New York, 1975.
  3. H. Reiter, L1-algebras and Segal algebras, Lecture Notes in Mathematics, Vol. 231, Springer-Verlag, Berlin, 1971.
  4. H. Reiter and J. D. Stegeman, Classical harmonic analysis and locally compact groups, second edition, London Mathematical Society Monographs. New Series, 22, The Clarendon Press, Oxford University Press, New York, 2000.
  5. W. Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley and Sons), New York, 1962.