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Measures with natural spectra on locally compact abelian groups
Author(s):
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  whose Fourier-Stieltjes transforms vanish at infinity is closed under addition if and only if  is compact.
References:
- 1.
- J. Eschmeier, K. B. Laursen and M. M. Neumann, Multipliers with Natural Local Spectra on Commutative Banach algebras, Jour. Funct. Anal. 138 (1996), 273-294. MR 97g:46066
- 2.
- E. Hewitt and K. A. Ross, Abstract Harmonic Analysis II, Springer-Verlag 1970. MR 41:7378
- 3.
- M. M. Neumann, Banach algebras, decomposable convolution operators, and a spectral mapping property, Function Spaces, Marcel Dekker, New York, 1992, 307-323. MR 93e:46057
- 4.
- W. Rudin, Fourier-Stieltjes transforms of measures on independent sets, Bull. Amer. Math. Soc. 66 (1960), 199-202. MR 22:9802
- 5.
- N. Varopoulos, Sur les mesures de Radon d'un groupe localement compact abelian, C. R. Acad. Sci. Paris, Sér. A 258 (1964), 3805-3808. MR 28:4386
- 6.
- J .H .Williamson, A theorem on algebras of measures on topological groups, Proc. Edinburgh Philos. Soc. 11 (1959), 195-206. MR 22:2851
- 7.
- M .Zafran, On the spectra of multipliers, Pacific J. Math. 47 (1973), 609-626. MR 48:4653
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Additional 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
Email:
hatori@math.sc.niigata-u.ac.jp
DOI:
10.1090/S0002-9939-98-04288-9
PII:
S 0002-9939(98)04288-9
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
Copyright of article:
Copyright
1998,
American Mathematical Society
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