Related papers: Free pluriharmonic majorants and noncommutative in…
We define the Hardy spaces of free noncommutative functions on the noncommutative polydisc and the noncommutative ball and study their basic properties. Our technique combines the general methods of noncommutative function theory and…
In this paper, we study free pluriharmonic functions on noncommutative balls, and their boundary behavior. The main tools used in this study are certain noncommutative transforms which are introduced in the present paper and which…
We obtain a noncommutative multivariable analogue of Louhichi and Olofsson characterization of Toeplitz operators with harmonic symbols on the weighted Bergman space $A_m({\bf D})$, as well as Eschmeier and Langendorfer extension to the…
We solve the commutant lifting and interpolation problems in the setting of the Hardy space and Schur functions on the open unit ball of $\mathbb{C}^n$. Our solutions also signify the role of inner functions on the unit ball, objects whose…
We develop a theory of holomorphic functions in several noncommuting (free) variables and thus provide a framework for the study of arbitrary n-tuples of operators. The main topics are the following: Free holomorphic functions and Hausdorff…
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…
In this paper we initiate the study of composition operators on the noncommutative Hardy space $H^2_{\bf ball}$. Several classical results about composition operators (boundedness, norm estimates, spectral properties, compactness,…
We initiate the study of weighted multi-Toeplitz operators associated with noncommutative regular domains in B(H)^n. These operators are acting on the full Fock space with n generators and have as symbols free pluriharmonic functions.…
This paper concerns a commutant lifting theorem and a Nevanlinna-Pick type interpolation result in the setting of multipliers from vector-valued Drury-Arveson space to a large class of vector-valued reproducing kernel Hilbert spaces over…
We study the multiplier algebras $A(\mathcal{H})$ obtained as the closure of the polynomials on certain reproducing kernel Hilbert spaces $\mathcal{H}$ on the ball $\mathbb{B}_d$ of $\mathbb{C}^d$. Our results apply, in particular, to the…
In this paper we begin the study of Schur analysis and de Branges-Rovnyak spaces in the framework of Fueter hyperholomorphic functions. The difference with other approaches is that we consider the class of functions spanned by Appell-like…
In this article we study commutant lifting, more generally intertwining lifting, for different reproducing kernel Hilbert spaces over two domains in $\mathbb{C}^n$, namely the unit ball and the unit polydisc. The reproducing kernel Hilbert…
In this expository paper we describe the study of certain non-self-adjoint operator algebras, the Hardy algebras, and their representation theory. We view these algebras as algebras of (operator valued) functions on their spaces of…
The main purpose of this paper is to investigate characterizations of composition operators on Bloch and Hardy type spaces. Initially, we use general doubling weights to study the composition operators from harmonic Bloch type spaces on the…
The goal of the present paper is to introduce and study noncommutative Hardy spaces associated with the regular $\Lambda$-polyball, to develop a functional calculus on noncommutative Hardy spaces for the completely non-coisometric (c.n.c.)…
We study several aspects concerning slice regular functions mapping the quaternionic open unit ball into itself. We characterize these functions in terms of their Taylor coefficients at the origin and identify them as contractive…
We define the corresponding Hardy space, Schur multipliers and their realizations, and interpolation. Possible applications of the present work include matrices of quaternions, matrices of split quaternions, and other algebras of…
In the present paper we introduce a new concept of Hardy type space naturally defined on the Klein-Dirac quadric. We study different properties of the functions belonging to these spaces, in particular boundary value problems. We apply…
In this paper we continue the study of free holomorphic functions on the unit ball of B(H)^n, where B(H) is the algebra of all bounded linear operators on a Hilbert space H. Several classical results from complex analysis have free…
In a recent paper, we introduced and studied the class of admissible noncommutative domains $D_{g^{-1}}(H)$ in $B(H)^n$ associated with admissible free holomorphic functions $g$ in noncommutative indeterminates $Z_1,\ldots, Z_n$. Each such…