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arXiv · 1807.01178

Enhanced Laplace transform and holomorphic Paley-Wiener-type theorems

Christophe Dubussy
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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.

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Christophe Dubussy. 2019-06-17. Enhanced Laplace transform and holomorphic Paley-Wiener-type theorems. https://doi.org/10.4171/rsmup%2F36

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