Generalization of an Eneström-Kakeya type theorem to the quaternions

Robert Gardner

Received N/A; revised N/A; accepted N/A

This work is licensed under Creative Commons Attribution–NonCommercial International License (CC BY-NC 4.0).

The well-known Eneström-Kakeya theorem states that polynomial p(z)=∑nν=0aνzνp(z)=∑ν=0naνzν, where 0≤a0≤a1≤⋯≤an0≤a0≤a1≤⋯≤an, has all of its (complex) zeros in |z|≤1|z|≤1. Many generalizations of this result exist in the literature. In this paper, we extend one such result to the quaternionic setting and state one of the possible corollaries.

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Generalization of an Eneström-Kakeya type theorem to the quaternions

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