On asymptotic Gauss-Lucas theorem

2015/10/08 by R. Boegvad, Dmitry Khavinson, D. Khavinson +5
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #math.CA

paper · pdf · doi:10.48550/arxiv.1510.02339

4 pages, 2 figures

arxiv created 2015/10/08 · openalex publication_date 2015/10/08 · arxiv updated 2015/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we extend the Gauss-Lucas theorem on the zeros of the derivative of a univariate polynomial to the case of sequences of univariate polynomials whose almost all zeros lie in a given convex bounded domain in C.

Related

• Strengthening the Gauss-Lucas theorem for polynomials with Zeros in the interior of the convex hull
• Analogue of Gauss-Lucas theorem for non convex set on the complex plane
• On approximate Gauss-Lucas theorems
• Multivariate Gauss-Lucas Theorems
• A Stability Version of the Gauss-Lucas Theorem and Applications