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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Singular measures with absolutely
continuous convolution squares
on locally compact groups


Author: Antonis Bisbas
Journal: Proc. Amer. Math. Soc. 127 (1999), 2865-2869
MSC (1991): Primary 43A05
Published electronically: April 23, 1999
MathSciNet review: 1600100
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Abstract | References | Similar Articles | Additional Information

Abstract: Saeki's result states that on any locally compact nondiscrete group there exist continuous singular measures, with respect to the left Haar measure, $\mu $ with $\mu * \mu $ in $L^{p}$ for all $p, \;1\leq p < \infty $. This paper gives a new and short proof of this using Rademacher-Riesz products.


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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: http://dx.doi.org/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
Published electronically: April 23, 1999
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 1999 American Mathematical Society