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June 2001 Decompositions of Measures on Compact Abelian Groups
Tokyo J. Math. 24(1): 13-18 (June 2001). DOI: 10.3836/tjm/1255958308


It is shown that the set of finite regular Borel measures with natural spectra for a compact abelian group $\mathfrak{G}$ is closed under addition if and only if $\mathfrak{G}$ is discrete. If $G$ is a non-discrete locally compact abelian group, then there exists a finite regular Borel measure with natural spectrum such that the corresponding multiplication operator on $L^1(G)$ is not decomposable.


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Osamu HATORI. Enji SATO. "Decompositions of Measures on Compact Abelian Groups." Tokyo J. Math. 24 (1) 13 - 18, June 2001.


Published: June 2001
First available in Project Euclid: 19 October 2009

zbMATH: 1014.43001
MathSciNet: MR1844414
Digital Object Identifier: 10.3836/tjm/1255958308

Rights: Copyright © 2001 Publication Committee for the Tokyo Journal of Mathematics

Vol.24 • No. 1 • June 2001
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