J Austral Math Soc Ser A 48 pp57--65, 1990.

A Note on Riesz Sets and Lacunary Sets

R. G. M. Brummelhuis

Abstract

W. Rudin has proved that the union of the Riesz set N Í R with a L(1)-subset of Z is again a Riesz set. In this note we generalize his result to compact groups whose center contains a circle group, thereby extending an earlier F. and M. Riesz theorem for such groups by the author. We also investigate the possibility of constructing L(p)-sets for these groups, departing from L(p)-sets for the circle group in the center.

1980 AMS Subject Classification (1985 Revision): primary 43A05, 43A30, 43A46; secondary 22E30, 43A77

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Authors

R. G. M. Brummelhuis

Department of Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands.