Convexity properties of twisted root maps (Q1011035)

The author presents a general setting for the study of the geometry of zeros of polynomials and their distributions under the action of various classes of linear operators. In particular he proves that the twisted root maps associated with linear operators acting on the manifold \(H_n\) of monic hyperbolic polynomials of degree \(n\) are Gårding convex on every polynomial pencil and characterize the class of polynomial pencils of logarithmic derivative type by means of the strong spectral order. He also proposes a conjecture for complex polynomials.