The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on February 10, 2015 at 14:00 in Room 478 of IMI.

A talk on:

Proof of the Sector Theorem

will be delivered by Acad. Blagovest Sendov.

Everybody is invited.

Abstract:

Absract: Let S(φ)={z : |arg(z)|≥φ} be a sector on the complex plane. If φ≥π/2, then S(φ) is a convex set and, according to Gauss-Lucas theorem, if all the zeros of the polynomial p(z) are on the sector S(φ), then the same is true for the zeros of all its derivatives. In the lecture it is proved that, if the polynomial p(z) is with real and non negative coefficients, then the same is true also for φ<π/2, when the sector is not a convex set.