相关论文: A note on interpolation in the generalized Schur c…

We construct interpolation operators for functions taking values in a symmetric space -- a smooth manifold with an inversion symmetry about every point. Key to our construction is the observation that every symmetric space can be realized…

The goal of this paper is to develop the theory of Schur complementation in the context of operators acting on anti-dual pairs. As a byproduct, we obtain a natural generalization of the parallel sum and parallel difference, as well as the…

We introduce the multiple zeta functions with structures similar to those of symmetric functions such as Schur $P$-, Schur $Q$-, symplectic and orthogonal functions in the representation theory. We first consider their basic properties such…

We prove a real interpolation characterization for some non Euclidean H\"older spaces, built on the Lie structure induced by a class of ultra-parabolic Kolmogorov-type operators satisfying the H\"ormander condition. As a by-product we also…

In this paper we would like to show the interrelation between the different mathematical theories concerning the Schur interpolation problem, contractions in Hilbert spaces, pseudocontinuation and Darlington synthesis. The main objects of…

We give a complete characterization of limiting interpolation spa\-ces for the real method of interpolation using extrapolation theory. For this purpose the usual tools (e.g., Boyd indices or the boundedness of Hardy type operators) are not…

The class of Schur-Agler functions over a domain ${\mathcal D} \subset {\mathbb C}^{d}$ is defined as the class of holomorphic operator-valued functions on ${\mathcal D}$ for which a certain von Neumann inequality is satisfied when a…

We introduce generalized Schur functions and generalized positive functions in setting of slice hyperholomorphic functions and study their realizations in terms of associated reproducing kernel Pontryagin spaces

In a purely multi-variable setting (i.e., the issues discussed in this note are not interesting in the single variable operator theory setting), we show that the coincidence of two operator valued Schur class multipliers of a certain kind…

It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we…

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…

We present the abstract framework and some applications of interpolation theory. The main new result concerns interpolation between H^1 and L^p estimates for analytic families of operators acting on Schwartz functions.

We here first study the state space realization of a tensor-product of a pair of rational functions. At the expense of "inflating" the dimensions, we recover the classical expressions for realization of a regular product of rational…

This expository thesis contains a study of four interpolation theorems, the requisite background material, and a few applications. The materials introduced in the first three sections of Chapter 1 are used to motivate and prove the…

In the spectral theory of non-self-adjoint operators there is a well-known operation of product of operator colligations. Many similar operations appear in the theory of infinite-dimensional groups as multiplications of double cosets. We…

Three boundary Nevanlinna-Pick interpolation problems at finitely many points are formulated for generalized Schur functions. For each problem, the set of all solutions is parametrized in terms of a linear fractional transformation with a…

In this paper, we study functional approximations where we choose the so-called radial basis function method and more specifically, quasi-interpolation. From the various available approaches to the latter, we form new quasi-Lagrange…

Theory interpolation has found several successful applications in model checking. We present a novel method for computing interpolants for ground formulas in the theory of equality. The method produces interpolants from colored congruence…

We give a controllable energy-preserving and an observable co-energy-preserving de Branges-Rovnyak functional model realization of an arbitrary given operator Schur function defined on the complex right-half plane. We work the theory out…

We consider the problem of obtaining interpolation constraints for function classes, i.e., necessary and sufficient constraints that a set of points, function values and (sub)gradients must satisfy to ensure the existence of a global…