Weighted Big Lipschitz algebras of analytic functions and closed ideals

We give the smallest closed ideal with given hull and inner factor for some weighted big Lipschitz algebras of analytic functions

Closed ideals in analytic weighted Lipschitz algebras

We obtain a complete description of closed ideals in weighted Lipschitz algebras $\Lambda_\omega$ of analytic functions on the unit disk satisfying the following condition $$\frac{|f(z)-f(w)|}{\omega(|z-w|)}=o(1)\qquad(as |z-w| \longrightarrow 0),$$ where $\omega$ is a modulus of continuity satisfying some regularity conditions.Comment: 22 page

Closed ideals in some algebras of analytic functions

We obtain a complete description of closed ideals of the algebra \mathcal{D}\cap \mathrm{lip}_\alpha}, $0<\alpha\leq{1/2},$ where $\mathcal{D}$ is the Dirichlet space and \mathrm{lip}_\alpha} is the algebra of analytic functions satisfying the Lipschitz condition of order $\alpha.$Comment: 19 page

Idéaux fermés de certaines algèbres de fonctions analytiques.

In this thesis, we are interested to descrip the closed ideals in some algebras of analytic functions on the complex unit disk or polydisk.Dans cette thèse, nous nous intéressons à la description des idéaux fermés de certaines algèbres de fonctions analytiques sur le disque et le polydisque unité

HELSON SETS, SPECTRAL SYNTHESIS AND APPLICATIONS TO OPERATORS

In this paper we highlight the role played by Helson sets and/or sets of spectral synthesis in some recent results in operator theory. We consider in particular the results on the cyclicity in L p spaces, the Katznelson-Tzafriri type theorems and polynomially bounded operators

On closed ideals in the big Lipschitz algebras of analytic functions

In this paper we study the closed ideals in the big Lipschitz algebras of analytic functions on the unit disk. More precisely we give the smallest closed ideal with given hull and inner factor.

Idéaux fermés d'algèbres de Beurling analytiques sur le bidisque

International audienceWe 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 $f$