Let G be a compact group
and let Γ be the set of equivalence classes of the continuous irreducible unitary
representations of G. For γ ∈ Γ denote by χγ the character of γ, then for E ⊂ Γ any
function of the form ∑j=1nanχγn(γ1,⋯,γn∈ Eand a1,⋯,αn∈ C) will
be called a central E-polynomial, and the set of all such functions will be
denoted z𝒯E≈. A sel E ⊂ Γ is a central Sidon set when the norms ∥∥∞
and ∥∥A (∥f∥A=∑|αn|, where f =∑anχγn) are equivalent on Z𝒯E−,
and it is a central Λ(p) set when the norms ∥∥1 and ∥∥p are equivalent on
zFE. When G is abelian the algebraic structure of Λ(p) and Sidon set has
been studied extensively. In this paper the structure of central Λ(p) sets is
investigated in terms of the hypergroup structure of Γ. In particular it is
shown that central Λ(p)(p > 2) sets cannot contain arbitrarily long arithmetic
progressions.”
