Title :

Idéaux fermés d'algèbres de Beurling analytiques sur le bidisque

Author(s) :

Bouya, Brahim [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
El-Fallah, Omar [Auteur]
Kellay, Karim [Auteur]
Laboratoire d'Analyse, Topologie, Probabilités [LATP]

Journal title :

Bulletin des Sciences Mathématiques

Pages :

588-604

Publisher :

Elsevier

Publication date :

2010

ISSN :

0007-4497

English keyword(s) :

Beurling algebras
closed ideals
Bézout's identity

HAL domain(s) :

Mathématiques [math]/Variables complexes [math.CV]
Mathématiques [math]/Analyse fonctionnelle [math.FA]

English abstract : [en]

We study the closed ideal in the Beurling algebras $\aA^{+}_{\alpha,\beta}$ of holomorphic function $f$ in the bidisc such that $$\sum\limits_{n,m\geq 0} |\widehat{f}(n,m)|(1+n)^{\alpha}(1+m)^\beta<\infty.$$ We characterize ...
Show more >We study the closed ideal in the Beurling algebras $\aA^{+}_{\alpha,\beta}$ of holomorphic function $f$ in the bidisc such that $$\sum\limits_{n,m\geq 0} |\widehat{f}(n,m)|(1+n)^{\alpha}(1+m)^\beta<\infty.$$ We characterize the functions $f\in \aA^+_{\alpha,\beta}$, under a restriction on their zero sets, such that the closed ideal generated by $f$ coincides with the ideal of all functions vanishing on the zero set of $f$.Show less >

Language :

Français

Popular science :

Non

ANR Project :

Dynamique des opérateurs

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL