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

Alexander V. Abanin; Le Hai Khoi

doi:10.1016/j.crma.2009.06.008

Complex Analysis

On the duality between

A^{- \infty} (D)

and

A_{D}^{- \infty}

for convex domains

Presented by: Jean-Pierre Demailly

Alexander V. Abanin ¹; Le Hai Khoi 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, Volume 347 (2009) no. 15-16, pp. 863-866.

Abstract
Résumé

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.

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.

Received: 2009-04-12
Accepted: 2009-06-08
Published online: 2009-07-02

DOI: 10.1016/j.crma.2009.06.008

Author's affiliations:

Alexander V. Abanin ¹; Le Hai Khoi 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

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     author = {Alexander V. Abanin and Le Hai Khoi},
     title = {On the duality between $ {A}^{-\infty }(D)$ and $ {A}_{D}^{-\infty }$ for convex domains},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {863--866},
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     language = {en},
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Alexander V. Abanin; Le Hai Khoi. On the duality between $ {A}^{-\infty }(D)$ and $ {A}_{D}^{-\infty }$ for convex domains. Comptes Rendus. Mathématique, Volume 347 (2009) no. 15-16, pp. 863-866. doi : 10.1016/j.crma.2009.06.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.06.008/

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