Related papers: A note on interpolation in the generalized Schur c…

The main goal of this paper is to demonstrate the usefulness of certain ideas from System Theory in the study of problems from complex analysis. With this paper, we also aim to encourage analysts, who might not be familiar with System…

Passive discrete-time systems in Pontryagin space setting are investigated. In this case the transfer functions of passive systems, or characteristic functions of contractive operator colligations, are generalized Schur functions. The…

We introduce a Schur-Agler type class associated with the tetrablock and establish a realization theorem for this class. Furthermore, we provide a tetrablock analog of the interpolation theorem, extension theorem, and the Toeplitz corona…

We extend Agler's notion of a function algebra defined in terms of test functions to include products, in analogy with the practice in real algebraic geometry, and hence the term preordering in the title. This is done over abstract sets and…

A seminal result of Agler characterizes the so-called Schur-Agler class of functions on the polydisk in terms of a unitary colligation transfer function representation. We generalize this to the unit ball of the algebra of multipliers for a…

An indefinite variant of the abstract interpolation problem is considered. Associated to this problem is a model Pontryagin space isometric operator V. All the solutions of the problem are shown to be in a one-to-one correspondence with a…

This note comprises a synthesis of certain results in the theory of exact interpolation between Hilbert spaces. In particular, we examine various characterizations of interpolation spaces and their relations to a number of results in…

We provide necessary and sufficient conditions for operator-valued functions on arbitrary sets associated with a collection of test functions to have factorizations in several situations.

The notion of a unitary realization is used to estimate derivatives of arbitrary order of functions in the Schur-Agler class on the polydisk and unit ball.

Following ideas from the Abstract Interpolation Problem of Katsnelson et al. (Operators in spaces of functions and problems in function theory, vol 146, pp 83-69, Naukova Dumka, Keiv, 1987) for Schur class functions, we study a general…

Classical Schur analysis is intimately connected to the theory of orthogonal polynomials on the circle [Simon, 2005]. We investigate here the connection between multipoint Schur analysis and orthogonal rational functions. Specifically, we…

Limiting real interpolation method is applied to describe the behaviour of the Fourier coefficients of functions that belong to spaces which are "very close" to L2.

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…

In this paper we study the consequences of overinterpolation, i.e., the situation when a function can be interpolated by polynomial, or rational, or algebraic functions in more points that normally expected. We show that in many cases such…

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…

This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…

We develop the convergence theory for a well-known method for the interpolation of functions on the real axis with rational functions. Precise new error estimates for the interpolant are de- rived using existing theory for trigonometric…

Jim Agler revolutionized the area of Pick interpolation with his realization theorem for what is now called the Agler-Schur class for the unit ball in $\mathbb C^d$. We discuss an extension of these results to algebras of functions arising…

We show that for integral operators of general form the norm bounds in Lorentz spaces imply certain norm bounds for the maximal function. As a consequence, the a.e. convergence for the integral operators on the Lorentz spaces follows from…

We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A…