Measures with natural spectra on locally compact abelian groups

Hatori, Osamu

doi:10.1090/S0002-9939-98-04288-9

Measures with natural spectra on locally compact abelian groups
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Proc. Amer. Math. Soc. 126 (1998), 2351-2353 Request permission

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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