Nuij Sequences for Garding Hyperbolic Polynomials

TL;DR

This paper investigates operators that preserve hyperbolicity in polynomials, building on classical and recent work to deepen understanding of hyperbolic polynomial spaces.

Contribution

It provides new results on hyperbolicity preserving operators on polynomial spaces, extending Nuij's work and following recent developments by Kurdyka and Paunescu.

Findings

Characterization of hyperbolicity preserving operators

Extension of Nuij's results on hyperbolic polynomials

New insights into the structure of hyperbolic polynomial spaces

Abstract

Hyperbolic polynomials were first introduced by Garding in 1959 in [2]. The space of this type of polynomial was studied by Nuij and various results were given in [4]. Following the work of Kurdyka and Paunescu in [3], this paper gives a result on hyperbolicity preserving operators on the space of polynomials.