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Singular measures with absolutely continuous convolution squares on locally compact groups
Author(s):
Antonis
Bisbas
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2865-2869.
MSC (1991):
Primary 43A05
Posted:
April 23, 1999
MathSciNet review:
1600100
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Abstract:
Saeki's result states that on any locally compact nondiscrete group there exist continuous singular measures, with respect to the left Haar measure,  with  in  for all  . This paper gives a new and short proof of this using Rademacher-Riesz products.
References:
- [1]
- A. Bisbas and C. Karanikas, On the continuity of measures, Applicable Analysis, Vol 48 (1993), 23-35. MR 95e:43001
- [2]
- A. H. Dooley and S. K. Gupta, Continuous singular measures with absolutely continuous convolution squares, Proceedings of the American Math. Soc. Vol. 124, 10, (1996), 3115 - 3122. MR 96m:43011
- [3]
- C. C. Graham and O. C. McGehee, Essays in Commutative Harmonic Analysis, Springer-Verlag, New York 1979. MR 81d:43001
- [4]
- E. Hewitt and H. Zuckerman, Singular measures with absolutely continuous convolution squares, Proc. Cambridge Phil. Soc. 62 (1966), 339-420; 63, (1967), 367-368. MR 33:1655
- [5]
- C. Karanikas, Examples of Riesz products-type measures on metrizable groups, Boll. Un. Math. Ital. 7, 4-A (1990), 331-341. MR 92d:43002
- [6]
- C. Karanikas and S. Koumandos, Continuous singular measures with absolutely continuous convolution squares on locally compact groups, Illinois J. of Math. 35 (3) (1991), 490-495. MR 92b:43004
- [7]
- D. L. Ragozin, Central measures on compact simple Lie groups, J. of Functional Analysis 10 (1972), 212-229. MR 49:5715
- [8]
- S. Saeki, Singular measures having absolutely continuous convolution powers, Illinois J. of Math. 21 (1977), 395-412. MR 58:6719
- [9]
- N. Wiener and A. Wintner, Fourier-Stieltjes transforms and singular infinite convolutions, Amer. J. Math., vol. 60 (1938), 513-522.
- [10]
- J. H. Williamson, A theorem on algebras of measures on topological groups, Proc. Edinburgh Math. Soc., vol. 11 (1958/59), 195 - 206. MR 22:2851
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Additional Information:
Antonis
Bisbas
Affiliation:
Department of Mathematics, University of the Aegean, Karlovasi 83200, Samos, Greece
Address at time of publication:
Technological Education Institute of Kozani, School of Technological Applications, General Department, Kila 50100, Kozani, Greece
Email:
bisbas@kozani.teikoz.gr
DOI:
10.1090/S0002-9939-99-04827-3
PII:
S 0002-9939(99)04827-3
Keywords:
Singular measures,
Rademacher functions
Received by editor(s):
June 25, 1997
Received by editor(s) in revised form:
December 3, 1997
Posted:
April 23, 1999
Communicated by:
Christopher D. Sogge
Copyright of article:
Copyright
1999,
American Mathematical Society
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