Vol. 50, No. 1, 1974

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ISSN: 0030-8730
On the hypergroup structure of central Λ(p) sets

George Benke

Vol. 50 (1974), No. 1, 19–27

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,n Eand a1,n 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 (fA = |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.”

Mathematical Subject Classification 2000
Primary: 43A46
Received: 27 September 1972
Revised: 31 January 1973
Published: 1 January 1974
George Benke