Hokkaido Mathematical Journal

YAMAGUCHI Hiroshi,

On a result of Saeki-Takahashi and a theorem of Bochner.

Hokkaido Mathematical Journal, 38 (2009) pp.497-510

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Abstract

Saeki extended the F. and M. Riesz theorem to $\mathbb{R}^N$ $(N \geqq 2)$, and Takahashi extended Saeki's result to a LCA group. We give a result, which is relevant to theirs. We also give a strong version of Bochner's generalization of the F. and M. Riesz theorem.

MSC(Primary)43A05
MSC(Secondary)43A10, 43A25
Uncontrolled KeywordsLCA group, measure, Fourier transform, quasi-invariant.