Free holomorphic functions and interpolation

TL;DR

This paper develops a noncommutative multivariable version of the classical Nevanlinna-Pick interpolation problem, extending it to operator-valued functions on the unit ball in complex n-space.

Contribution

It introduces a noncommutative multivariable analogue of the Nevanlinna-Pick interpolation problem for functions with positive real parts.

Findings

Derived operator-valued analytic interpolation results on the unit ball in C^n

Extended classical interpolation theory to noncommutative multivariable setting

Provided new tools for operator-valued function analysis

Abstract

In this paper we obtain a noncommutative multivariable analogue of the classical Nevanlinna-Pick interpolation problem for analytic functions with positive real parts on the open unit disc. As consequences, we deduce some results concerning operator-valued analytic interpolation on the unit ball on C^n.