Analytic theory of polynomials

TL;DR: In this paper, the critical points of the polynomial equation 1 and 2 in the upper half-plane of the imaginary axis of the plane were studied, where the gaps between the roots of (1) and (2) were shown to increase as one proceeds upward.

TL;DR: In this article, the robust Schur-stability problem of a disk polynomial with coefficients depended on parameters varying in a compact set was studied. And the authors proved that Schurstability of such polynomials can be reduced to constructing a set of polytopic sequences under the assumption that the parameters have the polytopic structure.

TL;DR: In this paper, the properties of stable polynomials in several variables with real or complex coefficients are defined in terms of where the polynomial is non-vanishing.