Properties of the set of hadamardized Hurwitz polynomials (Q1666360)

Summary: We say that a Hurwitz polynomial \(p \left(t\right)\) is a Hadamardized polynomial if there are two Hurwitz polynomials \(f \left(t\right)\) and \(g \left(t\right)\) such that \(f \ast g = p\), where \(f \ast g\) is the Hadamard product of \(f\) and \(g\). In this paper, we prove that the set of all Hadamardized Hurwitz polynomials is an open, unbounded, nonconvex, and arc-connected set. Furthermore, we give a result so that a fourth-degree Hurwitz interval polynomial is a Hadamardized polynomial family and we discuss an approach of differential topology in the study of the set of Hadamardized Hurwitz polynomials.