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2 results

  • I0 SETS FOR COMPACT, CONNECTED GROUPS: INTERPOLATION WITH MEASURES THAT ARE NONNEGATIVE OR OF SMALL SUPPORT

  • Part of
  • COLIN C. GRAHAM, KATHRYN E. HARE
  • Journal:
    Journal of the Australian Mathematical Society / Volume 84 / Issue 2 / April 2008
    Published online by Cambridge University Press:
    01 April 2008, pp. 199-215
    Print publication:
    April 2008
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  • In the dual object of an infinite compact, connected group, every infinite Sidon set contains an infinite subset on which full interpolation can be performed using very small classes of measures (discrete measures on arbitrarily small sets or nonnegative discrete measures). In particular, the Figà-Talamanca–Rider subset of an infinite product of compact, connected, simple Lie groups has these kinds of interpolation. This substantially improves previous interpolation results.

  • A general criterion for the existence of infinite Sidon sets

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  • David C. Wilson
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 45 / Issue 1 / August 1988
    Published online by Cambridge University Press:
    09 April 2009, pp. 11-29
    Print publication:
    August 1988
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  • Let G be any compact group, connected or disconnected, with dual object Ĝ. We define a family of local Sidon subsets of Ĝ in terms of allowable images of the representations. Using this family we develop a straightforward criterion whereby the existence of infinite Sidon subsets of Ĝ may be decided.