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arXiv · 2001.02676

On the existence of Hurwitz polynomials with no Hadamard factorization

Stanisław Białas·Michał Góra
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Abstract

A Hurwitz stable polynomial of degree $n\geq1$ has a Hadamard factorization if it is a Hadamard product (i.e. element-wise multiplication) of two Hurwitz stable polynomials of degree $n$. It is known that Hurwitz stable polynomials of degrees less than four have a Hadamard factorization. We show that for arbitrary $n\geq4$ there exists a Hurwitz stable polynomial of degree $n$ which does not have a Hadamard factorization.

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Stanisław Białas, Michał Góra. 2020-01-08. On the existence of Hurwitz polynomials with no Hadamard factorization. https://arxiv.org/abs/2001.02676

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