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A Paley–Wiener theorem for convex sets in Cn

✍ Scribed by Niklas Lindholm

Publisher
Elsevier Science
Year
2002
Tongue
French
Weight
206 KB
Volume
126
Category
Article
ISSN
0007-4497

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✦ Synopsis

We study the Laplace transform on Hardy spaces on a class of convex domains in C n . We obtain a Paley-Wiener theorem with a norm that characterizes the entire functions of exponential type which occur as Laplace transforms. This is done by using the Fantappiè transform and the Borel transform to rewrite the Laplace transform and reduce the problem to known theorems in one complex variable.  2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved.

Résumé

Nous étudions la transformée de Laplace dans des espace de Hardy sur des domaines convexes et lisses dans C n . Nous obtenons un théorème de type Paley-Wiener, avec une norme qui caractérise les fonctions holomorphes de type exponentiel obtenues comme des transformées de Laplace.

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