The Enestrom-Kakeya Theorem for polynomials of a quaternionic variable

JOURNAL OF APPROXIMATION THEORY

卷:250

Article

Carney, N.¹  Gardner, R.¹  Keaton, R.¹  Powers, A.¹ 

[1] East Tennessee State Univ, Dept Math & Stat, Johnson City, TN 37614 USA

关键词: Enestrom-Kakeya Theorem;    Zeros of polynomials;    Quaternions;   

DOI  :  10.1016/j.jat.2019.105325

来源: Elsevier

【 摘 要 】

The well-known Enestrom-Kakeya Theorem states that a polynomial with real, nonnegative, monotone increasing coefficients has all its complex zeros in the closed unit disk in the complex plane. In this paper, we extend this result by showing that all quaternionic zeros of such a polynomial lie in the unit sphere in the quaternions. We also extend related results from the complex to quaternionic setting. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free