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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Measures with natural spectra
on locally compact abelian groups

Author: Osamu Hatori
Journal: Proc. Amer. Math. Soc. 126 (1998), 2351-2353
MSC (1991): Primary 43A10, 43A25
MathSciNet review: 1443389
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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.

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Osamu Hatori
Affiliation: Department of Mathematical Sciences, Graduate School of Science and Technology, Niigata University, 8050 Ikarashi 2-no-chou, Niigata, 950-21 Japan

Keywords: Natural spectrum, locally compact abelian group
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
Article copyright: © Copyright 1998 American Mathematical Society