Necessary conditions for Hadamard factorizations of Hurwitz polynomials |
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Authors: | Carlos Arturo Loredo-Villalobos Baltazar Aguirre-Hernández [Author vitae] |
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Affiliation: | aDepartamento de Matemáticas, Universidad Autónoma Metropolitana–Iztapalapa, Av. San Rafael Atlixco no. 186, Col. Vicentina, Iztapalapa 09340, México, D.F., Mexico |
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Abstract: | A property of Hurwitz polynomials is related with the Hadamard product. Garloff and Wagner proved that Hadamard products of Hurwitz polynomials are Hurwitz polynomials, and Garloff and Shrinivasan shown that there are Hurwitz polynomials of degree 4 which do not have a Hadamard factorization into two Hurwitz polynomials of the same degree 4. In this paper, we give necessary conditions for an even-degree Hurwitz polynomial to have a Hadamard factorization into two even-degree Hurwitz polynomials; such conditions are given in terms of the coefficients of the given polynomial alone. Furthermore, we show that if an odd-degree Hurwitz polynomial has a Hadamard factorization then a system of nonlinear inequalities has at least one solution. |
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Keywords: | Hurwitz polynomials Hadamard product Hadamard factorization |
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