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Continuous singular measures
with absolutely continuous convolution squares

Authors: Anthony H. Dooley and Sanjiv Kumar Gupta
Journal: Proc. Amer. Math. Soc. 124 (1996), 3115-3122
MSC (1991): Primary 43A77
MathSciNet review: 1328346
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove for every non-abelian compact connected group $G$ there is a continuous, singular, central measure $\mu $ with $\mu *\mu $ in $L^{p}$ for all $p,\ 1 \leq p < \infty $. We also construct such measures on some families of non-abelian compact totally disconnected groups. These results settle an open question of Ragozin.

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Additional Information

Anthony H. Dooley
Affiliation: School of Mathematics, University of New South Wales, New South Wales 2052, Australia

Sanjiv Kumar Gupta
Affiliation: School of Mathematics, University of New South Wales, New South Wales 2052, Australia
Address at time of publication: Department of Mathematics, University of South Pacific, Suva, Fiji Islands

Received by editor(s): September 4, 1994
Received by editor(s) in revised form: April 3, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society