Non-negative polynomials without hyperbolic certificates of non-negativity
Year: 2026
Type: article
Abstract: In this paper we study the relationship between the set of all non-negative multivariate homogeneous polynomials and those, which we call hyperwrons, whose non-negativity can be deduced from an identity involving the Wronskians of hyperbolic polynomials. We give a sufficient condition on positive integers m and 2 y such that there are non-negative polynomials of degree 2 y in m variables that are not hyperwrons. Furthermore, we give an explicit example of a non-negative quartic form that is not a sum of hyperwrons. We partially extend our results to hyperzouts, which are polynomials whose non-negativity can be deduced from an identity involving the Bézoutians of hyperbolic polynomials.
Source: Advances in Geometry
Authors: H. L. Brian Ng, James Saunderson
Institution: Monash University
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,712
OpenAlex ID: W7139968655