Rational Matrix-Valued Pick Functions of Several Variables

TL;DR

This paper characterizes rational matrix-valued functions of multiple variables that maintain a nonnegative imaginary part in the upper poly-half-plane, providing matrix representations for such functions.

Contribution

It introduces matrix representations for rational matrix-valued functions with positive imaginary parts in several variables, extending classical single-variable results.

Findings

Derived explicit matrix representations for these functions.

Extended the theory of Pick functions to multiple variables.

Provided a framework for analyzing multivariable matrix-valued functions.

Abstract

For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.