Enhanced Laplace transform and holomorphic Paley-Wiener-type theorems

Abstract

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 Méril as limits of tempered Laplace-isomorphisms. In particular, we show how contour integrations naturally appear in this framework.