Inner functions and Pick-Nevanlinna interpolation in a multi-connected domain

TL;DR

This paper characterizes inner functions of finite order in multi-connected domains and extends Pick-Nevanlinna interpolation to Hermite type, providing a broader framework for complex analysis problems.

Contribution

It introduces a description of finite order inner functions in multi-connected domains and generalizes Pick-Nevanlinna interpolation to Hermite type, expanding existing theoretical tools.

Findings

Characterization of finite order inner functions in multi-connected domains

Generalization of Pick-Nevanlinna interpolation to Hermite type

Framework for optimization-based interpolation in complex analysis

Abstract

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.