Related papers: Boundary Nevanlinna-Pick interpolation via reducti…
In this paper we introduce the concept of matrix-valued $q$-rational functions. In comparison to the classic case we give different characterizations with principal emphasise on realizations and discuss algebraic manipulations. We also…
The nondegenerate Nevanlinna-Pick-Carath\'eodory-Fejer interpolation problem with finitely many interpolation conditions always has infinitely many solutions in a generalized Schur class $\cS_\kappa$ for every $\kappa\ge \kappa_{\rm min}$…
Given a domain $\Omega$ in $\mathbb{C}^m$, and a finite set of points $z_1,\ldots, z_n\in \Omega$ and $w_1,\ldots, w_n\in \mathbb{D}$ (the open unit disc in the complex plane), the $Pick\, interpolation\, problem$ asks when there is a…
In this paper we study the Nevanlinna-Pick matrix interpolation problem in the Carath\'eodory class with infinite data (both in the nondegenerate and degenerate cases). We develop the Sz\"okefalvi-Nagy and Kor\'anyi operator approach to…
Given a domain $\Omega$ in $\mathbb{C}^m$, and a finite set of points $z_1,z_2,\ldots, z_n\in \Omega$ and $w_1,w_2,\ldots, w_n\in \mathbb{D}$ (the open unit disc in the complex plane), the \textit{Pick interpolation problem} asks when there…
We introduce a Julia implementation of the recently proposed Nevanlinna analytic continuation method. The method is based on Nevanlinna interpolants and, by construction, preserves the causality of a response function. For theoretical…
In this paper we address the problem of interpolating a spline developable patch bounded by a given spline curve and the first and the last rulings of the developable surface. In order to complete the boundary of the patch a second spline…
If $\fA$ is a unital weak-$*$ closed algebra of multiplication operators on a reproducing kernel Hilbert space which has the property $\bA_1(1)$, then the cyclic invariant subspaces index a Nevanlinna-Pick family of kernels. This yields an…
We give a solution to Pick's interpolation problem on the unit polydisc in $\mathbb{C}^n$, $n\geq 2$, by characterizing all interpolation data that admit a $\mathbb{D}$-valued interpolant, in terms of a family of positive-definite kernels…
The theory of Nevanlinna-Pick and Carath\'eodory-Fej\'er interpolation for matrix- and operator-valued Schur class functions on the unit disk is now well established. Recent work has produced extensions of the theory to a variety of…
We report on a general purpose method for the scalar Stefan problem inspired by the standard boundary updating method used in several existence proofs. By suitably modifying it we can solve numerically any kind of Stefan problem. We present…
This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…
We introduce a "dual-space approach" to mixed Nevanlinna-Pick/Carath\'eodory-Schur interpolation in Banach spaces X of holomorphic functions on the disk. Our approach can be viewed as complementary to the well-known commutant lifting…
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…
It is very elementary to observe that functions interpolating an extremal two-point Pick problem on the polydisc are just left inverses to complex geodesics. In the present article we show that the same property holds for a three-point Pick…
A modification of the well-known step-by-step process for solving Nevanlinna-Pick problems in the class of $\bR_0$-functions gives rise to a linear pencil $H-\lambda J$, where $H$ and $J$ are Hermitian tridiagonal matrices. First, we show…
We extend our Nevanlinna-Pick theorem for Hardy algebras and their representations to cover interpolation at the absolutely continuous points of the boundaries of their discs of representations. The Lyapunov order plays a crucial role in…
We give a new solvability criterion for the boundary Carath\'{e}odory-Fej\'{e}r problem: given a point $x \in \mathbb{R}$ and, a finite set of target values $a^0,a^1,...,a^n \in \mathbb{R}$, to construct a function $f$ in the Pick class…
The synthesis of optimization algorithms typically follows a design-first-analyze-later approach, which often obscures fundamental performance limitations and hinders the systematic design of algorithms operating at the achievable…
Unitary matrix-valued functions of frequency are matrix all-pass systems, since they preserve the norm of the input vector signals. Typically, such systems are represented and analyzed using their unitary-matrix valued frequency domain…