We present some results connected with estimation of the coefficients for some special class of functions holomorphic in the unit disc and defined by subordination to some multivalent functions.

We study connected components of a common zero set of equivalent singular inner functions in the maximal ideal space of the Banach algebra of bounded analytic functions on the open unit disk. To study topological properties of zero sets of inner functions, we give a new type of factorization theorem for inner functions.

We study a certain operator of multiplication by monomials in the weighted Bergman space both in the unit disk of the complex plane and in the polydisk of the $n$-dimensional complex plane. Characterization of the commutant of such operators is given.

We characterize compact composition operators acting on weighted Bergman-Orlicz spaces ${}_{\alpha }^{\psi }=f\in H\left(\right):{\int }_{}\psi \left(\right|f\left(z\right)\left|\right)d{A}_{\alpha }\left(z\right)<\infty$, where α > -1 and ψ is a strictly increasing, subadditive convex function defined on [0,∞) and satisfying ψ(0) = 0, the growth condition $li{m}_{t\to \infty }\psi \left(t\right)/t=\infty$ and the Δ₂-condition. In fact, we prove that $C_{\phi }$ is compact on ${}_{\alpha }^{\psi }$ if and only if it is compact on the weighted Bergman space ${²}_{\alpha }$.

Let K be a compact connected subset of cc, not reduced to a point, and F a univalent map in a neighborhood of K such that F(K) = K. This work presents a study and a classification of the dynamics of F in a neighborhood of K. When ℂ K has one or two connected components, it is proved that there is a natural rotation number associated with the dynamics. If this rotation number is irrational, the situation is close to that of “degenerate Siegel disks” or “degenerate Herman rings” studied by R. Pérez-Marco...

In this paper we study the comparative growth properties of a composition of entire and meromorphic functions on the basis of the relative order (relative lower order) of Wronskians generated by entire and meromorphic functions.

We describe the complete interpolating sequences for the Paley-Wiener spaces Lπp (1 &lt; p &lt; ∞) in terms of Muckenhoupt's (Ap) condition. For p = 2, this description coincides with those given by Pavlov [9], Nikol'skii [8] and Minkin [7] of the unconditional bases of complex exponentials in L2(-π,π). While the techniques of these authors are linked to the Hilbert space geometry of Lπ2, our method of proof is based in turning the problem into one about boundedness of the Hilbert transform...

It is proved that if the increasing sequence kn n=0..∞ n=0 of nonnegative integers has density greater than 1/2 and D is an arbitrary simply connected subregion of CRthen the system of Hermite associated functions Gkn(z) n=0..∞ is complete in the space H(D) of complex functions holomorphic in D.

We characterize, in terms of the Beurling-Malliavin density, the discrete spectra Λ ⊂ R for which a generator exists, that is a function φ ∈ L1(R) such that its Λ translates φ(x - λ), λ ∈ Λ, span L1(R). It is shown that these spectra coincide with the uniqueness sets for certain analytic clases. We also present examples of discrete spectra Λ ∈ R which do not admit a single generator while they admit a pair of generators.

Soit ${\left({\lambda }_n\right)}_{n\ge 1}$ une suite de Blaschke du disque unité $𝔻$ et $\Theta$ une fonction intérieure. On suppose que la suite de noyaux reproduisants ${\left(k_{\Theta }(z,{\lambda }_n):=\frac{1-\overline{\Theta \left({\lambda }_n\right)}\Theta \left(z\right)}{1-\overline{{\lambda }_n}z}\right)}_{n\ge 1}$ est complète dans l’espace modèle $K_{\Theta }^p:=H^p\cap \Theta \overline{H_0^p}$, $1\&lt;p\&lt;+\infty$. On étudie, dans un premier temps, la stabilité de cette propriété de complétude, à la fois sous l’effet de perturbations des fréquences ${\left({\lambda }_n\right)}_{n\ge 1}$ mais également sous l’effet de perturbations de la fonction $\Theta$. On retrouve ainsi un certain nombre de résultats classiques sur les systèmes d’exponentielles. Puis, si on suppose de plus que la suite ...