SOS Polynomials and Matrix Representations of Rational Real Functions

TL;DR

This paper explores SOS polynomials and matrix representations of rational real functions, linking Artin's denominators to Hilbert's 17th problem and analyzing derivatives within the Nevanlinna class.

Contribution

It establishes that numerators of derivatives of rational functions in the Nevanlinna class are SOS polynomials, connecting algebraic properties with function classes.

Findings

Artin's denominators relate to Hilbert's 17th problem.

Numerators of derivatives in the Nevanlinna class are SOS polynomials.

Provides characteristic properties of these polynomials and their matrix representations.

Abstract

The characteristic properties of Artin's denominators in Hilbert's 17th problem are obtained. It is proved that numerators of partial derivative of rational real function from the Nevanlinna class are SOS polynomials.