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. $\mathfrak {L}(G)$ 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 $\mu$ on G such that ${\mu ^n}$ is singular-symmetric for $1 \leqslant n \leqslant k$ and ${\mu ^n} \in \mathfrak {L}(G)$ for $n > k$.