2019
DOI: 10.4171/rsmup/36
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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 Laplaceisomorphisms. In particular, we show how contour integrations naturally appear in this framework.Bât. B37, Analyse algébrique, Quartier Polytech 1, Allée de la découverte 12,

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“…In [5], we defined a natural notion of convolution between analytic functionals with noncompact convex carrier (generalizing the work of Méril in [13]) and showed compatibility with the additive holomorphic cohomological convolution, modulo some growth conditions. We also explained that this convolution is transformed into a product by the enhanced Laplace transform studied in [6]. Hence, the cohomological framework offers additional clarity concerning these contour-integration transformations.…”
Section: O(cmentioning
confidence: 95%
“…In [5], we defined a natural notion of convolution between analytic functionals with noncompact convex carrier (generalizing the work of Méril in [13]) and showed compatibility with the additive holomorphic cohomological convolution, modulo some growth conditions. We also explained that this convolution is transformed into a product by the enhanced Laplace transform studied in [6]. Hence, the cohomological framework offers additional clarity concerning these contour-integration transformations.…”
Section: O(cmentioning
confidence: 95%