Quasi-invariance of measures of analytic type on locally compact abelian groups

Abstract

Asmar, Montgomery-Smith and Saeki gave a generalization of a theorem of Bochner for a locally compact abelian group with certain direction. We show that a strong version of their result holds for a σ-compact, connected locally compact abelian group with certain direction. We also give several conditions for quasi-invariance of analytic measures and another proof of a theorem of deLeeuw and Glicksberg.