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2 results

  • CENTRAL INTERPOLATION SETS FOR COMPACT GROUPS AND HYPERGROUPS

  • DAVID GROW, KATHRYN E. HARE
  • Journal:
    Glasgow Mathematical Journal / Volume 51 / Issue 3 / September 2009
    Published online by Cambridge University Press:
    01 September 2009, pp. 593-603
    Print publication:
    September 2009
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  • We prove that every infinite subset of the dual of a compact, connected group contains an infinite, central, weighted I0 set. This yields a new proof of the fact that the duals of such groups admit infinite central p-Sidon sets for each p > 1. We also establish the existence of infinite, weighted I0 sets in the duals of many compact, abelian hypergroups.

  • Weighted p-Sidon sets

  • Part of
  • K. E. Hare, D. C. Wilson
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 61 / Issue 1 / August 1996
    Published online by Cambridge University Press:
    09 April 2009, pp. 73-95
    Print publication:
    August 1996
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  • A weighted generalization of a p-Sidon set, called an (a, p)-Sidon set, is introduced and studied for infinite, non-abelian, connected, compact groups G. The entire dual object Ĝ is shown never to be central (p − 1, p)-Sidon for 1 ≦ p < 2, nor central (1 + ε, 2)-Sidon for ε > 0. Local (p, p)-Sidon sets are shown to be identical to local Sidon sets. Examples are constructed of infinite non-Sidon sets which are central (2p − 1, p)-Sidon, or (p − 1, p)-Sidon, for 1 < p < 2. Full m-fold FTR sets are proved not to be central (a, 2m/(m + 1))-Sidon for any a > 1.