BOCHNER-SCHWARTZ THEOREM ON LOCALLY COMPACT ABELIAN GROUPS

  • Kim, Jin-Man (DEPARTMENT OF MATHEMATICS, SEOUL NATIONAL UNIVERSITY) ;
  • Cho, Jong-Gyu (DEPARTMENT OF MATHEMATICS, SEOUL NATIONAL UNIVERSITY)
  • Published : 2001.02.01

Abstract

We study the Fourier transformation on the Gelfand-Bruhat space of type S and characterize this space by means of Fourier transform on a locally compact abelian group G. Also, we extend Bochner-Schwartz theorem to the dual space of the Gelfand-Bruhat space and the space of Fourier hyperfunctions on G. respectively.

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