Related papers: New composition products for complex harmonic func…
In the present article a new method of deriving integral representations of combinations and partitions in terms of harmonic products has been established. This method may be relevant to statistical mechanics and to number theory.
We study compactness property of composition operator acting from a model space generated by an inner function to the Hardy space.
We realize norms of most composition operators acting on the Hardy space with linear fractional symbol as roots of hypergeometric functions. This realization leads to simple necessary and sufficient conditions on the symbol to exhibit…
Let H^2(D) denote the classical Hardy space of the open unit disk D in the complex plane. We obtain descriptions of both the spectrum and essential spectrum of composition operators on H^2(D) whose symbols belong to the class S(2)…
We show that there exist non-compact composition operators in the connected component of the compact ones on the classical Hardy space $H^2$ on the unit disc. This answers a question posed by Shapiro and Sundberg in 1990. We also establish…
In this paper we investigate the numerical ranges of composition operators whose symbols are elliptic automorphisms of finite orders, on the Hilbert Hardy space $H^2(D)$.
Compared with harmonic Bergman spaces, this paper introduces a new function space which is called the pluriharmonic Hardy space $h^{2}(\mathbb{T}^{2})$. We character (semi-) commuting Toeplitz operators on $h^{2}(\mathbb{T}^{2})$ with…
Let $\varphi$ be a linear fractional self-map of the open unit disk $\mathbb{D}$ and $H^2$ the Hardy space of analytic functions on $\mathbb{D}$. The goal of this article is to characterize the linear fractional composition operators…
We describe recent nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It…
This current article aims to study a new subclass of meromorphic functions with positive coefficients by reconstructing a new operator in the punctured open disc. Also, some geometric properties are considered and investigated, such results…
This paper considers discrete and continuous semigroups of (weighted) composition operators on the Fock space. For discrete semigroups consisting of powers of a single operator, the asymptotic behaviour of the semigroups is analysed. For…
In this paper we study the complex symmetry in the several variable Fock space by using the techniques of weighted composition operators and semigroups. We characterize unbounded weighted composition operators that are (real) complex…
In this paper we characterize some basic properties of composition operators on the spaces of harmonic Bloch functions. First we provide some equivalent conditions for boundedness and compactness of composition operators. Then by using…
Finite-dimensional model spaces are quotient spaces of the Hardy space on the open unit disc, determined by finite Blaschke products. Composition operators, on the other hand, act by composing Hardy space functions with analytic self-maps…
In this paper, we study composition operators on Hilbert space of complex-valued harmonic functions. In particular, we explore isometries, the type of self-map that generate bounded composition operator, and characterize the boundedness of…
In this paper, we study 2-complex symmetric composition operators with the conjugation $J$ on the Hardy space $H^2$. More precisely, we obtain the necessary and sufficient condition for the composition operator $C_\phi$ to be 2-complex…
We characterize the semigroups of composition operators that are strongly continuous on the mixed norm spaces $H(p,q,\alpha)$. First, we study the separable spaces $H(p,q,\alpha)$ with $q<\infty,$ that behave as the Hardy and Bergman…
In this paper, we study the basic properties such as boundedness and compactness of composition operators on discrete analogue of generalized Hardy space defined on a homogeneous rooted tree. Also, we compute the operator norm of…
In this paper, we introduce a new norm for $\mathcal{S}^2(\mathbb{D})$, encompassing functions whose first and second derivatives belong to both the Hardy space $\mathcal{H}^2(\mathbb{D})$ and the classical Bergman space…
Composition operators with analytic symbols on some reproducing kernel Hilbert spaces of entire functions on a complex Hilbert space are studied. The questions of their boundedness, seminormality and positivity are investigated. It is…