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  • A note on Riesz sets and lacunary sets

  • Part of
  • R. G. M. Brummelhuis
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 48 / Issue 1 / February 1990
    Published online by Cambridge University Press:
    09 April 2009, pp. 57-65
    Print publication:
    February 1990
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  • W. Rudin has proved that the union of the Riesz set N ⊆ R with a Λ(l)-subset of Z is again a Riesz set. In this note we generalize his result to compact groups whose 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 Λ(p)-sets for these groups, departing from Λ(p)-sets for the circle group in center.