Decompositions of Measures on Compact Abelian Groups
HATORI, Osamu ; SATO, Enji
Tokyo J. of Math., Tome 24 (2001) no. 2, p. 13-18 / Harvested from Project Euclid
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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.
Publié le : 2001-06-15
Classification:  
@article{1255958308,
     author = {HATORI, Osamu and SATO, Enji},
     title = {Decompositions of Measures on Compact Abelian Groups},
     journal = {Tokyo J. of Math.},
     volume = {24},
     number = {2},
     year = {2001},
     pages = { 13-18},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1255958308}
}

HATORI, Osamu; SATO, Enji. Decompositions of Measures on Compact Abelian Groups. Tokyo J. of Math., Tome 24 (2001) no. 2, pp.  13-18. http://gdmltest.u-ga.fr/item/1255958308/