Definition 2

Let $n\geqslant 1$ be an integer and let $\boldsymbol{a}\in A^n$. Let U be an open neighbourhood of Sp$^n(\boldsymbol{a})$. One says that a family $\boldsymbol{a}'$ is an envelope of $(\boldsymbol{a},U)$ if $\boldsymbol{a}'\in \mathbf{C}^{n+p}$ extends $\boldsymbol{a}$ and if $U\times \mathbf{C}^p$ contains the polynomially convex envelope of Sp$^{n+p}(\boldsymbol{a}')$.