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.
