On iterates of convolutions

Abstract

Let μ \mu be a signed measure, of total variation one, on a locally compact Abelian group. We study in this note the ideal I = { τ : τ ≪ m a n d | | μ n ∗ τ | | → 0 } I = \{ \tau :\tau \ll m\;and\; ||{\mu ^n} \ast \tau || \to 0\} where m m is the Haar measure.