Measures with natural spectra on locally compact abelian groups
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- by Osamu Hatori
- Proc. Amer. Math. Soc. 126 (1998), 2351-2353
- DOI: https://doi.org/10.1090/S0002-9939-98-04288-9
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Abstract:
Every bounded regular Borel measure on noncompact LCA groups is a sum of an absolutely continuous measure and a measure with natural spectrum. The set of bounded regular Borel measures with natural spectrum on a nondiscrete LCA group $G$ whose Fourier-Stieltjes transforms vanish at infinity is closed under addition if and only if $G$ is compact.References
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Bibliographic Information
- Osamu Hatori
- Affiliation: Department of Mathematical Sciences, Graduate School of Science and Technology, Niigata University, 8050 Ikarashi 2-no-chou, Niigata, 950-21 Japan
- MR Author ID: 199931
- Email: hatori@math.sc.niigata-u.ac.jp
- Received by editor(s): September 19, 1996
- Received by editor(s) in revised form: January 20, 1997
- Additional Notes: The author was partially supported by the Grants-in Aid for Scientific Research, The Ministry of Education, Science and Culture, Japan
- Communicated by: J. Marshall Ash
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2351-2353
- MSC (1991): Primary 43A10, 43A25
- DOI: https://doi.org/10.1090/S0002-9939-98-04288-9
- MathSciNet review: 1443389