On a dual to the properties of Hurwitz polynomials I

Gastón Vergara-Hermosilla (1)

1 IMB - Institut de Mathématiques de Bordeaux

In this paper we develop necessary and sufficient conditions for describe the family of anti-Hurwitz polynomials, introduced by Vergara-Hermosilla et al. in [9]. 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.

Domaines: Mathématiques [math]

Gastón Vergara-Hermosilla. On a dual to the properties of Hurwitz polynomials I. 2020. ⟨hal-02519924v2⟩