TITLE:
On a Dual to the Properties of Hurwitz Polynomials I
AUTHORS:
Gastón Vergara-Hermosilla
KEYWORDS:
Hurwitz Polynomials, Anti-Hurwitz Polynomials, Hermite-Biehler Theo-rem, Exclusion Principle
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.11 No.1,
March
17,
2021
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.