Vania Mascioni

Learn More
The celebrated Gauss-Lucas theorem states that all the roots of the derivative of a complex non-constant polynomial p lie in the convex hull of the roots of p, called the Lucas polygon of p. We improve the Gauss-Lucas theorem by proving that all the nontrivial roots of p lie in a smaller convex polygon which is obtained by a strict contraction of the Lucas(More)
We provide a unified, elementary, topological approach to the classical results stating the continuity of the complex roots of a polynomial with respect to its coefficients, and the continuity of the coefficients with respect to the roots. In fact, endowing the space of monic polynomials of a fixed degree n and the space of n roots with suitable topologies,(More)
Let Pn be the complex vector space of all polynomials of degree at most n. We give several characterizations of the linear operators T : Pn → Pn for which there exists a constant C > 0 such that for all nonconstant f ∈ Pn there exist a root u of f and a root v of T f with |u − v| ≤ C. We prove that such perturbations leave the degree unchanged and, for a(More)
  • 1