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The object of this paper is to show that AP(G) and W(G) are algebras for a restricted class of compact groups called groups of bounded representation type. Let G be a compact non-Abelian group; we let G denote the set of equivalence classes of continuous unitary irreducible representations of G. We call G the dual of G. For aeG, let T a be an element of a. Then T a is a homomorphism of G into U(n a ), the group of n a x n a unitary matrices, where n a is the dimension of a. We use TJp)t odoi:10.1017/s0305004100050568 fatcat:majbkic2gvgpraerqoxj56myn4