Properties of the Set of Hadamardized Hurwitz Polynomials

Abstract EN

We say that a Hurwitz polynomial pt is a Hadamardized polynomial if there are two Hurwitz polynomialsft and gt such that f∗g=p, where f∗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 intervalpolynomial is a Hadamardized polynomial family and we discuss an approach of differential topology in thestudy of the set of Hadamardized Hurwitz polynomials.