Hokkaido Mathematical Journal

YAMAGUCHI Hiroshi,

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

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
MSC(Secondary)43A10, 43A25
Uncontrolled KeywordsLCA group, measure, Fourier transform, quasi-invariant