Enhanced Laplace transform and holomorphic Paley-Wiener-type theorems
arXiv:1807.01178 · doi:10.4171/RSMUP/36
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.
Final version. To appear in "Rendiconti del Seminario Matematico della Università di Padova", 23 pages