Holomorphic reflexivity of exponential analytic functionals

Let $G$ be a compactly generated complex Lie group, and let $\mathscr A_{\exp}(G)$ denote the topological algebra of exponential analytic functionals on $G$. Holomorphic reflexivity is the duality property considered in the paper.

Exponential analytic functional conjecture. The algebra

$$\mathscr A_{\exp}(G)$$

is holomorphically reflexive.

The source states that this conjecture follows from the preceding Banach-algebra linearity conjecture and is therefore open in general.