Darlington's Theorem for Rational Nevanlinna Functions in Several Variables

TL;DR

This paper explores the extension of Darlington's theorem to rational Nevanlinna functions in multiple variables, revealing their structure as Cayley inner functions in higher dimensions.

Contribution

It establishes a new connection between rational Nevanlinna functions and Cayley inner functions in several variables, generalizing classical results.

Findings

Rational Nevanlinna functions are Cayley inner functions in n+1 variables.

The paper provides a characterization of these functions in multiple variables.

It extends Darlington's theorem to a multivariable setting.

Abstract

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.