Hurwitz matrices of doubly infinite series
arXiv:1608.04440 · doi:10.1016/j.laa.2017.05.012
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.
15 pages