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arXiv · 1608.04440

Hurwitz matrices of doubly infinite series

Alexander Dyachenko
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Abstract

This paper aims at extending the criterion that the quasi-stability of a polynomial is equivalent to the total nonnegativity of its Hurwitz matrix. We give a complete description of functions generating doubly infinite series with totally nonnegative Hurwitz and Hurwitz-type matrices (in a Hurwitz-type matrix odd and even rows come from two distinct power series). The corresponding result for singly infinite series is known: it is based on a certain factorization of Hurwitz-type matrices, which is absent in the doubly infinite case. A necessary condition for total nonnegativity of generalized Hurwitz matrices follows as an application.

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Alexander Dyachenko. 2016-08-15. Hurwitz matrices of doubly infinite series. https://doi.org/10.1016/j.laa.2017.05.012

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