  In the Gelfand-Shilov setting, the localisation operator
$A^{\varphi_1,\varphi_2}_a$ is equal to the Weyl operator whose symbol is the
convolution of $a$ with the Wigner transform of the windows $\varphi_2$ and
$\varphi_1$. We employ this fact, to extend the definition of localisation
operators to symbols $a$ having very fast super-exponential growth by allowing
them to be mappings from ${\mathcal D}^{\{M_p\}}(\mathbb R^d)$ into ${\mathcal
D}'^{\{M_p\}}(\mathbb R^d)$, where $M_p$, $p\in\mathbb N$, is a
non-quasi-analytic Gevrey type sequence. By choosing the windows $\varphi_1$
and $\varphi_2$ appropriately, our main results show that one can consider
symbols with growth in position space of the form $\exp(\exp(l|\cdot|^q))$,
$l,q>0$.
