Enhanced Laplace transform and holomorphic Paley-Wiener-type theorems
Complex Variables
2019-06-18 v4
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 M\'{e}ril as limits of tempered Laplace-isomorphisms. In particular, we show how contour integrations naturally appear in this framework.
Keywords
Cite
@article{arxiv.1807.01178,
title = {Enhanced Laplace transform and holomorphic Paley-Wiener-type theorems},
author = {Christophe Dubussy},
journal= {arXiv preprint arXiv:1807.01178},
year = {2019}
}
Comments
Final version. To appear in "Rendiconti del Seminario Matematico della Universit\`a di Padova", 23 pages