On two refinements of the Gauss-Lucas theorem
Abstract
In this note, we give a new proof of a refinement of the Gauss-Lucas theorem given in [6]. The new proof uses a technique used to produce and older refinement of the same theorem in [3]. It was observed that the two refinements are complimentary to each other and we hope that this work explains why this is so.
2020 Mathematics Subject Classification:
30C10Keywords
Geometry of Polynomials, Gauss-Lucas theorem, Schur-Szegö’s composition theorem, polar convexity, Specht, Krawtchouk, Dimitrov
Author Details
Hristo Sendov
Department of Statistical and Actuarial Sciences
Department of Mathematics
Western University
1151 Richmond Str.
London, ON, N6A 5B7 Canada
e-mail: hsendov@uwo.ca
References
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