On the Gauss-Lucas theorem in the quaternionic setting
Complex Variables
2017-11-08 v1
Abstract
In theory of one complex variable, Gauss-Lucas Theorem states that the critical points of a non constant polynomial belong to the convex hull of the set of zeros of the polynomial. The exact analogue of this result cannot hold, in general, in the quaternionic case; instead, the critical points of a non constant polynomial belong to the convex hull of the set of zeros of the so-called symmetrization of the given polynomial. An incomplete proof of this statement was given in [8]. In this paper we present a different but complete proof of this theorem and we discuss a consequence.
Cite
@article{arxiv.1711.02157,
title = {On the Gauss-Lucas theorem in the quaternionic setting},
author = {Sorin G. Gal and J. Oscar González-Cervantes and Irene Sabadini},
journal= {arXiv preprint arXiv:1711.02157},
year = {2017}
}