Related papers: Characteristic Function, Schur Interpolation Probl…
The main aim of this paper is to establish the connection between well-known criteria for the pseudocontinuability of a non-inner Schur function Theta in the unit disk. In a canonical way we associate a probability measure mu on the unit…
Let $\mathfrak M$ and $\mathfrak N$ be separable Hilbert spaces and let $\Theta(\lambda)$ be a function from the Schur class ${\bf S}(\mathfrak M,\mathfrak N)$ of contractive functions holomorphic on the unit disk. The operator…
The Darlington synthesis problem (in the scalar case) is the problem of embedding a given contractive analytic function to an inner $2\times 2$ matrix function as the entry. A fundamental result of Arov--Douglas--Helton relates this…
The operator-valued Schur-class is defined to be the set of holomorphic functions $S$ mapping the unit disk into the space of contraction operators between two Hilbert spaces. There are a number of alternate characterizations: the operator…
We introduce the notion of characteristic functions for commuting tuples of hypercontractions on Hilbert spaces, as a generalization of the notion of Sz.-Nagy and Foias characteristic functions of contractions. We present an explicit method…
The Schur-Agler class consists of functions over a domain satisfying an appropriate von Neumann inequality. Originally defined over the polydisk, the idea has been extended to general domains in multivariable complex Euclidean space with…
We analyse two special cases of $\mu$-synthesis problems which can be reduced to interpolation problems in the set of analytic functions from the disc into the symmetrised bidisc and into the tetrablock. For these inhomogeneous domains we…
Bitangential interpolation problems in the class of matrix valued functions in the generalized Schur class are considered in both the open unit disc and the open right half plane, including problems in which the solutions is not assumed to…
The Schur class, denoted by $\mathcal{S}(\mathbb{D})$, is the set of all functions analytic and bounded by one in modulus in the open unit disc $\mathbb{D}$ in the complex plane $\mathbb{C}$, that is \[ \mathcal{S}(\mathbb{D}) = \{\varphi…
In the PhD thesis of the second author under the supervision of the third author was defined the class SI of J-contractive functions, depending on a parameter and arising as transfer functions of overdetermined conservative 2D systems…
Characteristic functions of linear operators are analytic functions that serve as complete unitary invariants. Such functions, as long as they are built in a natural and canonical manner, provide representations of inner functions on a…
We present a set of algebraic relations among Schur functions which are a multi-time generalization of the ``discrete Hirota relations'' known to hold among the Schur functions of rectangular partitions. We prove the relations as an…
An indefinite generalization of Nudel'man's problem is used in a systematic approach to interpolation theorems for generalized Schur and Nevanlinna functions with interior and boundary data. Besides results on existence criteria for…
We introduce Schur multiple zeta functions which interpolate both the multiple zeta and multiple zeta-star functions of the Euler-Zagier type combinatorially. We first study their basic properties including a region of absolute convergence…
We study factorizations of operator valued functions of weighted Schur classes over multiply-connected domains. There is a correspondence between functions from weighted Schur classes and so-called ``conservative curved'' systems introduced…
Let $E$ be a $W^{\ast}$-correspondence over a von Neumann algebra $M$ and let $H^{\infty}(E)$ be the associated Hardy algebra. If $\sigma$ is a faithful normal representation of $M$ on a Hilbert space $H$, then one may form the dual…
The CMV matrices and their sub-matrices are applied to the description of all solutions to the Schur interpolation problem for contractive analytic operator-valued functions in the unit disk (the Schur class functions).
Characterization of Schur-class functions (analytic and bounded by one in modulus on the open unit disk) in terms of their Taylor coefficients at the origin is due to I. Schur. We present a boundary analog of this result: necessary and…
We investigate the behavior of a generalized Hilbert space model of a function in the Schur class of the bidisk at singular boundary points that satisfy a growth condition. We examine the relationship between the boundary behavior of Schur…
We define a number of related combinatorial objects, each of which possesses a surprising symmetry. We include several applications such as a combinatorial explanation for certain fixed points of the involution $\omega$ on the ring of…