Ideaux fermes d'algebres de Beurling analytiques sur le bidisque

Abstract

We study the closed ideal in the Beurling algebras ${\mathcal{A}}_{\alpha ,\beta }^{+}$ of holomorphic function $f$ in the bidisc such that ${\sum }_{n,m\ge 0}|\hat{f}(n,m)|(1+n{)}^{\alpha }(1+m{)}^{\beta }<+\infty$. We determine the function $f\in {\mathcal{A}}_{\alpha ,\beta }^{+}$ such that the ideals generated by $f$ coincide with the ideal generated by their zeros set.

17 pages