Related papers: Nevanlinna-Pick interpolation problem in the ball
We analyze the three point Pick interpolation problem on the bidisk
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 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.
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…
Consider a scaled Nevanlinna-Pick interpolation problem and let $\Pi$ be the Blaschke product whose zeros are the nodes of the problem. It is proved that if $\Pi$ belongs to a certain class of inner functions, then the extremal solutions of…
In this paper we formulate and solve Nevanlinna-Pick and Carath\'eodory type problems for tensor algebras with data given on the N-dimensional operator unit ball of a Hilbert space. We develop an approach based on the displacement structure…
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…
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…
Bounded holomorphic interpolation problems associated to finitely many data have, in general, distinct solutions. Uniqueness arises only in some convex extreme configurations. Rational inner functions in a polydisk are the best understood…
In this work we blend interpolation theory with numerical integration, constructing an interpolator based on integrals over $n$-dimensional balls. We show that, under hypotheses on the radius of the $n$-balls, the problem can be treated as…
New classes of generalized Nevanlinna functions, which under multiplication with an arbitrary fixed symmetric rational function remain generalized Nevanlinna functions, are introduced. Characterizations for these classes of functions are…
Given a collection $K$ of positive integers, let $H^{\infty}_K(\mathbb{D})$ denote the set of all bounded analytic functions defined on the unit disk $\mathbb{D}$ in $\mathbb{C}$ whose $k^{\text{th}}$ derivative vanishes at zero, for all $k…
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…
Every rational Nevanlinna function in n variables is a Cayley inner function in n + 1 variables with one variable fixed in the upper half-plane.
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…
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…
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…
The fundamental theorem on commutant lifting due to Sarason does not carry over to the setting of the polydisc. This paper presents two classifications of commutant lifting in several variables. The first classification links the lifting…
We settle the problem of finding an entire function with three singular values whose Nevanlinna characteristic dominates an arbitrarily prescribed function.
The problem of three particles interacting through harmonic forces is discussed within the Newtonian formalism. By means of a didactic approach, an exact analytical solution is found, and ways to extend it to the N-body case are pointed…