Related papers: A Constrained Nevanlinna-Pick Interpolation Proble…
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…
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…
In this paper, we will characterize those sets, over which every irreducible complete Nevanlinna--Pick space enjoys that its multiplier and supremum norms coincide. Moreover, we will prove that, if there exists an irreducible complete…
The connection between the standard $H^\infty$-problem in control theory and Nevanlinna-Pick interpolation in operator theory was established in the 1980s, and has led to a fruitful cross-pollination between the two fields since. In the…
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…
We show that any complete Nevanlinna-Pick space whose multiplier algebra has isometric Gelfand transform (or commutative C*-envelope) is essentially the Hardy space on the open unit disk.
We present certain existence criteria and parameterisations for an interpolation problem for completely positive maps that take given matrices from a finite set into prescribed matrices. Our approach uses density matrices associated to…
A general interpolation problem with operator argument is studied for functions f from the de Branges-Rovnyak space H(s) associated with an analytic function s mapping the open unit disk D into the closed unit disk. The interpolation…
We describe the set of inner functions of finite order in a multi-connected domain, then we consider an optimization formulation of the Pick-Nevanlinna interpolation problem, and we generalize it to Hermite type interpolation.
In the paper `Distinguished Varieties,' Agler and McCarthy used Hilbert function spaces to study the uniqueness properties of the Nevanlinna-Pick problem on the bidisc. In this work we give a geometric procedure for constructing a…
This paper concerns a commutant lifting theorem and a Nevanlinna-Pick type interpolation result in the setting of multipliers from vector-valued Drury-Arveson space to a large class of vector-valued reproducing kernel Hilbert spaces over…
In 2002 A.\ Hartmann and X.\ Massaneda obtained necessary and sufficient conditions for interpolation sequences for classes of analytic functions in the unit disc such that $\log M(r,f)=O((1-r)^{-\rho})$, $0<r<1$, $\rho \in (0 , +\infty)$,…
This survey shows how, for the Nevanlinna class N of the unit disc, one can define and often characterize the analogues of well-known objects and properties related to the algebra of bounded analytic functions $ H^\infty$: interpolating…
We show that the Hardy space on the unit disk is the only non-trivial irreducible reproducing kernel Hilbert space which satisfies the complete Nevanlinna-Pick property and hyponormality of all multiplication operators.
We prove a finiteness principle for interpolation of data by nonnegative Cm functions. Our result raises the hope that one can start to understand constrained interpolation problems in which e.g. the interpolating function F is required to…
We give a solvability criterion for a special case of the $\mu$-synthesis problem. That is, we prove the necessity and sufficiency of a condition for the existence of an analytic $2 \times 2$ matrix-valued function on the disc subject to a…
Given a sequence of points in the unit disk, a well known result due to Carleson states that if given any point of the sequence it is possible to interpolate the value one in that point and zero in all the other points of the sequence, with…
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 introduce the notion of a \lambda-nonisotropically balanced domain and show that the symmetrized polydisc in C^n, n \geq 2, is an example of such a domain. Given a \lambda-nonisotropically balanced domain \Omega, we derive effective…
We consider the following interpolation problem. Suppose one is given a finite set $E \subset \mathbb{R}^d$, a function $f: E \rightarrow \mathbb{R}$, and possibly the gradients of $f$ at the points of $E$. We want to interpolate the given…