Enhanced Laplace transform and holomorphic Paley-Wiener-type theorems

  • Christophe Dubussy

    Université de Liège, Belgium
Enhanced Laplace transform and holomorphic Paley-Wiener-type theorems cover

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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.

Cite this article

Christophe Dubussy, Enhanced Laplace transform and holomorphic Paley-Wiener-type theorems. Rend. Sem. Mat. Univ. Padova 142 (2019), pp. 181–209

DOI 10.4171/RSMUP/36