Vania Mascioni

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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)
Given a polynomial p of degree n ≥ 2 and with at least two distinct roots let Z(p) = {z : p(z) = 0}. For a fixed root α ∈ Z(p) we define the quantities ω(p, α) := min |α − v| : v ∈ Z(p) \ {α} and τ (p, α) := min |α − v| : v ∈ Z(p) \ {α}. We also define ω(p) and τ (p) to be the corresponding minima of ω(p, α) and τ (p, α) as α runs over Z(p). Our main(More)
We confirm two recent conjectures of W. Janous and thereby state the best possible form of the Erdös-Debrunner inequality for triangles. thus the area of the central triangle, while the other three are the areas of the " corner " triangles. The Erdös-Debrunner inequality states that at least one of the corner triangles has no greater area than the central(More)