Related papers: Composition-Differentiation Operator on Weighted B…
In this paper, we study the differentiation operator acting on discrete function spaces; that is spaces of functions defined on an infinite rooted tree. We discuss, through its connection with composition operators, the boundedness and…
We describe the spectrum of weighted $d$-isomorphisms of Banach lattices restricted on closed subspaces that are "rich" enough to preserve some "memory" of the order structure of the original lattice. The examples include (but are not…
Let $B_{n}$ be the unit ball in the complex vector space $\mathbb{C}^{n}$, and let $\varphi: B_{n}\rightarrow B_{n}$ be a holomorphic mapping. In this paper, we characterize those symbols $\varphi$ such that composition operators…
In this paper, we study the behavior of the singular values of Hankel operators on weighted Bergman spaces $A^2_{\omega _\varphi}$, where $\omega _\varphi= e^{-\varphi}$ and $\varphi$ is a subharmonic function. We consider compact Hankel…
We investigate composition operators on Hardy-Orlicz spaces when the Orlicz function $\Psi$ grows rapidly: compactness, weak compactness, to be $p$-summing, order bounded,..., and show how these notions behave according to the growth of…
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…
Formally symmetric differential operators on weighted Hardy-Hilbert spaces are analyzed, along with adjoint pairs of differential operators. Eigenvalue problems for such operators are rather special, but include many of the classical…
In this paper, a new characterization is provided for the boundedness, compactness and essential norm of the difference of two weighted composition operators on weighted-type spaces in the unit ball of $\mathbb{C}^n$.
In this paper, we give some estimates for the norm and essential norm of the differences of two composition operators between different Hardy spaces.
In this paper, we investigate the $\partial$-complex on weighted Bergman spaces on Hermitian manifolds satisfying a certain holomorphicity/duality condition. This generalizes the situation of the Segal-Bargmann space in $\mathbb{C}^n$,…
We study composition operators on the Hardy space $\mathcal{H}^2$ of Dirichlet series with square summable coefficients. Our main result is a necessary condition, in terms of a Nevanlinna-type counting function, for a certain class of…
We investigate composition-differentiation operators acting on the Dirichlet space of the unit disk. Specifically, we determine characterizations for bounded, compact, and Hilbert-Schmidt composition-differentiation operators. In addition,…
We investigate the compactness of composition operators on the Hardy space of Dirichlet series induced by a map $\varphi(s)=c_0s+\varphi_0(s)$, where $\varphi_0$ is a Dirichlet polynomial. Our results depend heavily on the characteristic…
We construct explicit differential operators on hermitian modular forms, extending methods developed for Siegel modular forms. These differential operators are closely related to the two-variable spherical pluriharmonic polynomials. We…
Let $\Omega\subset \mathbb{C}^n$ be a smooth bounded pseudoconvex domain and $A^2 (\Omega)$ denote its Bergman space. Let $P:L^2(\Omega)\longrightarrow A^2(\Omega)$ be the Bergman projection. For a measurable $\varphi:\Omega\longrightarrow…
In this paper, we focus on the weighted Bergman spaces $A_{\varphi}^{p}$ in $\mathbb{D}$ with $\varphi\in\mathcal{W}_{0}$. We first give characterizations of those finite positive Borel measures $\mu$ in $\mathbb{D}$ such that the embedding…
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…
Let $\mathcal{H}$ be a separable Hilbert space and let $A^{2}_{\varphi}(\mathcal{H})$ be the $\mathcal{H}$-valued Bergman spaces with exponential weights. In the present paper, we give the complete characterizations for the boundedness and…
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…
Previously, spectra of certain weighted composition operators on the Hardy Space were discovered under one of two hypotheses: either the compositional symbol converges under iteration to the Denjoy-Wolff point on all of the open disk rather…