Related papers: Algebras generated by two bounded holomorphic func…
A function which is analytic and bounded in the Unit disk is called a generator for the Hardy space or the Bergman space if polynomials in that function are dense in the corresponding space. We characterize generators in terms of sub-spaces…
We construct a Schauder basis for the space $Hol(\mathbb D)$, the space of holomorphic functions on the closed unit disk, consisting entirely of finite Blaschke products. The expansion coefficients are given explicitly. Our result remains…
Let $\Omega$ and $\Omega_{\fin}$ be the sets of all interpolating Blaschke products of type $G$ and of finite type $G$, respectively. Let $E$ and $E_{\fin}$ be the Douglas algebras generated by $H^\infty$ together with the complex…
We give a generalization of the notion of finite Blaschke products from the perspective of generalized inner functions in various reproducing kernel Hilbert spaces. Further, we study precisely how these functions relate to the so-called…
In this paper we study the function algebra generated by z^2 and g^2 on a small closed disk centered at the origin of the complex plane. We prove, using a biholomorphic change of coordinates and already developed techniques in this area,…
A closed subspace $\mathcal{M}$ of the Hardy space $H^2(\mathbb{D}^2)$ over the bidisk is called a submodule if it is invariant under multiplication by coordinate functions $z_1$ and $z_2$. Whether every finitely generated submodule is…
The initial motivation for this paper is to discuss a more concrete approach to an approximation theorem of Axler and Shields, which says that the uniform algebra on the closed unit disc closure(D) generated by z and h --- where h is a…
We show that the space of all bounded derivations from the disc algebra into its dual can be identified with the Hardy space $H^1$; using this, we infer that all such derivations are compact. Also, given a fixed derivation $D$, we construct…
We obtain boundedness from a product of Lebesgue or Hardy spaces into Hardy spaces under suitable cancellation conditions for a large class of multilinear operators that includes the Coifman-Meyer class, sums of products of linear…
Certain operator algebras A on a Hilbert space have the property that every densely defined linear transformation commuting with A is closable. Such algebras are said to have the closability property. They are important in the study of the…
A two-point algebra is a set of bounded analytic functions on the unit disk that agree at two distinct points $a,b \in \mathbb{D}$. This algebra serves as a multiplier algebra for the family of Hardy Hilbert spaces $H^2_t := \{ f\in H^2 :…
It is proved that exponential Blaschke products are the inner functions whose derivative is in the weak Hardy space. Exponential Blaschke products are described in terms of their logarithmic means and also in terms of the behavior of the…
We prove that the pointwise product of two holomorphic functions of the upper half-plane, one in the Hardy space $\mathcal H^1$, the other one in its dual, belongs to a Hardy type space. Conversely, every holomorphic function in this space…
By classical results of Herglotz and F. Riesz, any bounded analytic function in the complex unit disk has a unique inner-outer factorization. Here, a bounded analytic function is called \emph{inner} or \emph{outer} if multiplication by this…
Inner functions play a central role in function theory and operator theory on the Hardy space over the unit disk. Motivated by recent works of C. B\'en\'eteau et al. and of D. Seco, we discuss inner functions on more general weighted Hardy…
We prove that functions continuous up to the boundary are dense in de Branges-Rovnyak spaces induced by extreme points the unit ball of $H^\infty$.
In this paper K closedness is proved in the case of the couple of real Hardy spaces in the corresponding couple of Lebesgue spaces. This means roughly that any measurable decomposition of an analytic function gives rise to an "analytic"…
Given a complex domain $\Omega$ and analytic functions $\varphi_1,\ldots,\varphi_n : \Omega \to \mathbb{D}$, we give geometric conditions for $H^\infty(\Omega)$ to be generated by functions of the form $g \circ \varphi_k$, $g \in…
In this work, the density in $H(b)$ spaces of finitely connected planar domains and the boundedness of composition operators on these function spaces are studied. Density of the algebra $\mathcal{A}(D)$ is considered for both in the cases…
We derive lower bounds in best rational approximation of given degree to finite Blaschke products, in the Hardy space $H^2$ of the unit disk. We first consider approximation to $z^N$, and then move on to more general Blaschke products whose…