Enhanced Laplace transform and holomorphic Paley-Wiener-type theorems

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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.

Translated title of the contributionTransformation de Laplace enrichie et théorèmes de type Paley-Wiener
Original languageEnglish
Pages (from-to)181-209
Number of pages29
JournalRendiconti del Seminario Matematico della Università di Padova
Volume142
DOIs
Publication statusPublished - 11 Jun 2019
Externally publishedYes

Keywords

  • Laplace transform
  • Legendre transform
  • Enhanced subanalytic sheaves
  • Paley– Wiener-type theorems

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