Enhanced Laplace transform and holomorphic Paley-Wiener-type theorems

Christophe Dubussy

doi:10.4171/RSMUP/36

Enhanced Laplace transform and holomorphic Paley-Wiener-type theorems

Titre traduit de la contribution: Transformation de Laplace enrichie et théorèmes de type Paley-Wiener

Christophe Dubussy

Résultats de recherche: Contribution à un journal/une revue › Article › Revue par des pairs

Résumé

Partant d'une remarque concernant le calcul de la transformée de Laplace enrichie de Kashiwara-Schapira, utilisant le complexe de Dolbeault des distributions enrichies, nous expliquons comment obtenir des théorèmes de type Paley-Wiener explicites. En guise d'exemples, nous expliquons comment réobtenir certains théorèmes dus à Polya et Méril via des limites d'isomorphismes de Laplace tempérés. En particulier, nous montrons comment des intégrales de contour apparaissent naturellement dans ce contexte.

Titre traduit de la contribution	Transformation de Laplace enrichie et théorèmes de type Paley-Wiener
langue originale	Anglais
Pages (de - à)	181-209
Nombre de pages	29
journal	Rendiconti del Seminario Matematico della Università di Padova
Volume	142
Les DOIs	https://doi.org/10.4171/RSMUP/36
Etat de la publication	Publié - 11 juin 2019
Modification externe	Oui

mots-clés

Transformation de Laplace
Transformation de Legendre
Faisceaux sous-analytiques enrichis

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10.4171/RSMUP/36

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title = "Enhanced Laplace transform and holomorphic Paley-Wiener-type theorems",

abstract = "Starting from a remark about the computation of Kashiwara–Schapira{\textquoteright}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 = "Transformation de Laplace, Transformation de Legendre, Faisceaux sous-analytiques enrichis, Laplace transform, Legendre transform, Enhanced subanalytic sheaves, Paley– Wiener-type theorems",

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AB - 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.

KW - Transformation de Laplace

KW - Transformation de Legendre

KW - Faisceaux sous-analytiques enrichis

KW - Laplace transform

KW - Legendre transform

KW - Enhanced subanalytic sheaves

KW - Paley– Wiener-type theorems

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ER -

Enhanced Laplace transform and holomorphic Paley-Wiener-type theorems

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