On a Dual to the Properties of Hurwitz Polynomials I

Abstract

In this work we develop necessary and sufficient conditions for describing the family of anti-Hurwitz polynomials, introduced by Vergara-Hermosilla et al. in [1]. Specifically, we studied a dual version of the Theorem of Routh-Hurwitz and present explicit criteria for polynomials of low order and derivatives. Another contribution of this work is establishing a dual version of the Hermite-Biehler Theorem. To this aim, we give extensions of the boundary crossing Theorems and a zero exclusion principle for anti-Hurwitz polynomials.