# Hokkaido Mathematical Journal

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

PDF

### 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 43A10, 43A25 LCA group, measure, Fourier transform, quasi-invariant.