# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 43 (2014) pp.51-64

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### 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.

MSC(Primary) 43A05 43A10, 43A25 LCA group, measure, Fourier transform, quasi-invariant