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Singular measures with absolutely continuous convolution squares on locally compact groups

Authors:	Antonis Bisbas

Institution:	Department of Mathematics, University of the Aegean, Karlovasi 83200, Samos, Greece

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.

Keywords:	Singular measures Rademacher functions

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