On the duality between $ {A}^{-\infty }(D)$ and $ {A}_{D}^{-\infty }$ for convex domains

Abanin, Alexander V.; Khoi, Le Hai

doi:10.1016/j.crma.2009.06.008

Complex Analysis

On the duality between

A^{- \infty} (D)

and

A_{D}^{- \infty}

for convex domains
[Sur la dualité entre

A^{- \infty} (D)

A_{D}^{- \infty}

pour des domaines convexes]

Présenté par : Jean-Pierre Demailly

Abanin, Alexander V.¹ ; Khoi, Le Hai ²

¹ Southern Institute of Mathematics (SIM), Vladikavkaz 362027 and Southern Federal University (SFU), Rostov-on-Don 344090, The Russian Federation
² Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), 637371 Singapore

Comptes Rendus. Mathématique, Tome 347 (2009) no. 15-16, pp. 863-866.

Résumé
Abstract

Le but de cette Note est de démontrer que la transformation de Laplace des fonctionnelles analytiques établit une dualité mutuelle entre les espaces $A^{- \infty} (D)$ et $A_{D}^{- \infty}$ (D étant un domaine convexe borné dans $C^{N}$ ) et que des fonctions de $A_{D}^{- \infty}$ peuvent être représentées sous la forme de séries de Dirichlet avec fréquence de D.

The goal of this Note is to prove that the Laplace transformation of analytic functionals establishes the mutual duality between the spaces $A^{- \infty} (D)$ and $A_{D}^{- \infty}$ (D being a bounded convex domain in $C^{N}$ ) and that functions from $A_{D}^{- \infty}$ can be represented in a form of Dirichlet series with frequencies from D.

Reçu le : 2009-04-12
Accepté le : 2009-06-08
Publié le : 2009-07-02

DOI : 10.1016/j.crma.2009.06.008

Affiliations des auteurs :

Abanin, Alexander V. ¹ ; Khoi, Le Hai ²

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Abanin, Alexander V.; Khoi, Le Hai. On the duality between $ {A}^{-\infty }(D)$ and $ {A}_{D}^{-\infty }$ for convex domains. Comptes Rendus. Mathématique, Tome 347 (2009) no. 15-16, pp. 863-866. doi : 10.1016/j.crma.2009.06.008. http://archive.numdam.org/articles/10.1016/j.crma.2009.06.008/

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