Vol. 63, No. 1, 1976

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Weighted Sidon sets

Jeffery William Sanders

Vol. 63 (1976), No. 1, 255–279

A weighted generalisation of Sidon sets, W-Sidon sets, is introduced and studied for compact abelian groups. Firstly W-Sidon sets are characterised analogously to Sidon sets and variations of these characterisations shown to lead back to Sidon sets. For the circle group W-Sidon sets are constructed which are not Λ(1) and hence not Sidon. The algebra of all W’s making a set W-Sidon is investigated and Sidon and p-Sidon sets cast in terms of it. Finally analytic properties of W-Sidon sets are pursued and a necessary condition on the growth of W2 obtained.

Mathematical Subject Classification 2000
Primary: 43A46
Secondary: 42A44
Received: 6 May 1975
Published: 1 March 1976
Jeffery William Sanders