Related papers: A note on composition operators in a half-plane

Necessary and sufficient conditions are already known in the Hardy spaces of both the disc and the half plane for a composition operator to be an isometry, by Nordgren in the disc and by Chalendar and Partington in the half plane. All the…

We give a necessary and sufficient condition for a holomorphic self-map $\phi$ of the tridisc to induce a bounded composition operator on the associated Hardy space. This condition depends on the behaviour of the first and the second…

We give examples of composition operators $C\_\Phi$ on $H^2 (\D^2)$ showing that the condition $\|\Phi \|\_\infty = 1$ is not sufficient for their approximation numbers $a\_n (C\_\Phi)$ to satisfy $\lim\_{n \to \infty} [a\_n (C\_\Phi)…

As continuation of the study of polynomial approximation and composition operators on Dirichlet spaces of unit disk, which has settled a problem posed by Cima in 1976, the present paper aims to consider the case of the unbounded domains,…

Building on techniques used in the case of the disc, we use a variety of methods to develop formulae for the adjoints of composition operators on Hardy spaces of the upper half-plane. In doing so, we prove a slight extension of a known…

We construct an analytic self-map $\Phi$ of the bidisk ${\mathbb D}^2$ whose image touches the distinguished boundary, but whose approximation numbers of the associated composition operator on $H^2 ({\mathbb D}^2)$ are small in the sense…

We prove that a composition operator is bounded on the Hardy space $H^2$ of the right half-plane if and only if the inducing map fixes the point at infinity non-tangentially, and has a finite angular derivative $\lambda$ there. In this case…

We obtain a necessary and sufficient condition for a weighted composition operator to be co-isometric on a general weighted Hardy space of analytic functions in the unit disk whose reproducing kernel has the usual natural form. This turns…

Let $\Omega_1,\Omega_2\subset {\mathbb C}$ be bounded domains. Let $\phi:\Omega_1\rightarrow \Omega_2$ holomorphic in $\Omega_1$ and belonging to $W^{1,\infty}_{\Omega_2}(\Omega_1)$. We study the composition operators $f\mapsto f\circ\phi$…

In this work, we prove that weak compactness of composition operator on $H^{1}(U^{n})$ coincides with its compactness. We also characterize bounded and compact composition operators on $H^{1}(U^{n}).$\

In this paper we investigate the following problem: when a bounded analytic function $\phi$ on the unit disk $\mathbb{D}$, fixing 0, is such that $\{\phi^n : n = 0, 1, 2, . . . \}$ is orthogonal in $\mathbb{D}$?, and consider the problem of…

This paper studies the behaviour of iterates of weighted composition operators acting on spaces of analytic functions, with particular emphasis on the Hardy space $H^2$. Questions relating to uniform, strong and weak convergence are…

We study the composition operators of the Hardy space on D $\infty$ $\cap$ {\ell} 1 , the {\ell} 1 part of the infinite polydisk, and the behavior of their approximation numbers.

We investigate composition operators $C_{\Phi}$ on the Hardy-Smirnov space $H^{2}(\Omega)$ induced by analytic self-maps $\Phi$ of an open simply connected proper subset $\Omega$ of the complex plane. When the Riemann map…

We obtain necessary and sufficient conditions for the composition and weighted composition operator and product of composition operators to be isometry and unitary on $H_{E}(\xi).$ With the help of counter example we also prove that the…

Let X be a set of analytic functions on the open unit disk D, and let phi be an analytic function on D such that phi(D) is contained in D and f |-> f o phi takes X into itself. We present conditions on X ensuring that if f |-> f o phi is…

In this paper, we establish a compactness criterion for the composition-differentiation operator \( D_\Phi \) in terms of a decay condition of the mean counting function at the boundary of a half-plane. We provide a sufficient condition of…

We identify the semigroups consisting of bounded composition operators on the Hardy spaces $H^p(\U)$ of the upper half-plane. We show that any such semigroup is strongly continuous on $H^p(\U)$ but not uniformly continuous and we identify…

We consider the products of composition and differentiation operators on the Hardy space. We provide a complete characterization of the boundedness and compactness of these operators. Furthermore, we obtain the explicit condition for these…

In \cite{CO-Tp-spaces}, the present authors initiated the study of composition operators on discrete analogue of generalized Hardy space $\mathbb{T}_{p}$ defined on a homogeneous rooted tree. In this article, we give equivalent conditions…