Convolution powers of singular-symmetric measures. II

Abstract

Let G be an infinite compact abelian group such that its dual group contains an infinite independent subset. L ( G ) \mathfrak {L}(G) denotes the sum of all radicals of group algebras contained in the measure algebra on G. Then, for a positive integer k, there is a measure μ \mu on G such that μ n {\mu ^n} is singular-symmetric for 1 ⩽ n ⩽ k 1 \leqslant n \leqslant k and μ n ∈ L ( G ) {\mu ^n} \in \mathfrak {L}(G) for n > k n > k .