Related papers: Boundary Nevanlinna-Pick interpolation via reducti…
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…
We formulate three boundary Nevanlinna-Pick interpolation problems for generalized Nevanlinna functions. For each problem, we parameterize the set of all solutions in terms of a linear fractional transformation with an extended Nevanlinna…
Recent results of Davidson-Paulsen-Raghupathi-Singh give necessary and sufficient conditions for the existence of a solution to the Nevanlinna-Pick interpolation problem on the unit disk with the additional restriction that the interpolant…
Nevanlinna-Pick interpolation problem has been widely studied in recent decades, however, the known algorithm is not simplistic and robust enough. This paper provide a new method to solve the Nevanlinna-Pick interpolation problem with…
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…
The main results presented in this paper provide a complete and explicit description of all solutions to the left tangential operator Nevanlinna- Pick interpolation problem assuming the associated Pick operator is strictly positive. The…
A boundary Nevanlinna-Pick interpolation problem is posed and solved in the quaternionic setting. Given nonnegative real numbers $\kappa_1, \ldots, \kappa_N$, quaternions $p_1, \ldots, p_N$ all of modulus $1$, so that the $2$-spheres…
We give an elementary proof of a solvability criterion for the {\em boundary Carath\'{e}odory-Fej\'{e}r problem}: given a point $x \in \R$ and, a finite set of target values, to construct a function $f$ in the Pick class such that the first…
Nevanlinna-Pick interpolation and moment problems use the analytic structures provided by causality in order to provide rigorous bounds on smeared spectral functions. This proceedings discusses Nevanlinna-Pick interpolation and moment…
We prove the interpolation condition of S. Takahashi to the Nevanlinna-Pick-Caratheodory problem by using Sarason's theory.
We obtain necessary and sufficient conditions for Nevanlinna-Pick interpolation on the unit disk with the additional restriction that all analytic interpolating functions satisfy $f'(0)=0.$ Alternatively, these results can be interpreted as…
We give necessary and sufficient conditions for solving the spectral Nevanlinna--Pick lifting problem. This reduces the spectral Nevanlinna--Pick problem to a jet interpolation problem into the symmetrized polydisc.
Nevanlinna-Pick interpolation developed from a topic in classical complex analysis to a useful tool for solving various problems in control theory and electrical engineering. Over the years many extensions of the original problem were…
We revisit four approaches to the BiTangential Operator Argument Nevanlinna-Pick (BTOA-NP) interpolation theorem on the right half plane: (1) the state-space approach of Ball-Gohberg-Rodman, (2) the Fundamental Matrix Inequality approach of…
This article treats Nevanlinna-Pick interpolation in the setting of a special class of algebraic curves called distinguished varieties. An interpolation theorem, along with additional operator theoretic results, is given using a family of…
The goal of this note is to apply ideas from commutative algebra (a.k.a. affine algebraic geometry) to the question of constrained Nevanlinna-Pick interpolation. More precisely, we consider subalgebras $A \subset…
I describe a verifiable criterion for the solvability of the 2 by 2 spectral Nevanlinna-Pick problem with two interpolation points, and likewise for three other special cases of the mu-synthesis problem. The problem is to construct an…
We provide an effective single-matrix criterion, in terms of what we call the elementary Pick matrix, for the solvability of the noncommutative Nevanlinna-Pick interpolation problem in the row ball, and provide some applications. In…
We solve a three point Nevanlinna-Pick problem in the Euclidean ball. In particular, we determine a class of rational functions that interpolate this problem.
First, an abstract scheme of constructing biorthogonal rational systems related to some interpolation problems is proposed. We also present a modification of the famous step-by-step process of solving the Nevanlinna-Pick problems for…