Exercise 5, § 3

The family of distributions associated with the point measures $\varepsilon_n$ for $n\in \mathbf{Z}$ is summable in $\mathscr{S}'(\mathbf{R})$. Its sum $\omega$ satisfies $\mathscr{F}(\omega ) =\omega$. (This formula is equivalent to the Poisson formula for the locally compact group $G =\mathbf{R}^n$ endowed with the Lebesgue measure and the subgroup $H =\mathbf{Z}^n$, cf. II, § 1, No.$^o7.$)