Enhanced Laplace transform and holomorphic Paley-Wiener-type theorems
Dubussy, Christophe1
1 Université de Liège, Belgium
Rendiconti del Seminario Matematico della Università di Padova, Tome 142 (2019), pp. 181-209.
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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.

Publié le :
DOI : 10.4171/RSMUP/36
Classification : 44, 32, 35
Mots clés : Enhanced subanalytic sheaves, Laplace transform, Legendre transform, Paley– Wiener-type theorems
Dubussy, Christophe 1

1 Université de Liège, Belgium 
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     author = {Dubussy, Christophe},
     title = {Enhanced {Laplace} transform and holomorphic {Paley-Wiener-type} theorems},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {181--209},
     publisher = {European Mathematical Society Publishing House},
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Dubussy, Christophe. Enhanced Laplace transform and holomorphic Paley-Wiener-type theorems. Rendiconti del Seminario Matematico della Università di Padova, Tome 142 (2019), pp. 181-209. doi : 10.4171/RSMUP/36. http://archive.numdam.org/articles/10.4171/RSMUP/36/

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