Enhanced Laplace transform and holomorphic Paley-Wiener-type theorems

Starting from a remark about the computation of Kashiwara-Schapira’s enhanced Laplace transform by using the Dolbeault complex of enhanced distributions, we explain how to obtain explicit holomorphic Paley-Wiener-type theorems. As an example, we get back some classical theorems due to Polya and M'{e}ril as limits of tempered Laplace-isomorphisms. In particular, we show how contour integrations naturally appear in this framework.