CENTRAL INTERPOLATION SETS FOR COMPACT GROUPS AND HYPERGROUPS

Abstract

Abstract We prove that every infinite subset of the dual of a compact, connected group contains an infinite, central, weighted I 0 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 I 0 sets in the duals of many compact, abelian hypergroups.