Example

Suppose that $n= 1$. Let $a\in A$. For every open neighbourhood U of Sp($a$), there exists an infinitely differentiable mapping $h$ of $\mathbf{C}$ into $\mathbf{C}$ with compact support contained in U, equal to 1 in the neighbourhood of Sp($a$) (VAR, R1, p. 40, 5.3.6). Put

for $z\in \mathbf{C}-$ Sp($a$) and $u(z) = 0$ if $z\in$ Sp($a$). The pair $(h, u)$ is adapted to $a$ and the associated differential form is $\omega =du\wedge dz$.