An extension of the Hermite-Biehler theorem with application to polynomials with one positive root

Richard Ellard, Helena Šmigoc

If a real polynomial $f(x)=p(x^2)+xq(x^2)$ is Hurwitz stable (every root if $f$ lies in the open left half-plane), then the Hermite-Biehler Theorem says that the polynomials $p(-x^…