The Eneström–Kakeya Theorem for Polynomials of a Quaternionic Variable
The well-known Eneström–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.
Carney, N.; Gardner, Robert B.; Keaton, R.; and Powers, A.. 2020. The Eneström–Kakeya Theorem for Polynomials of a Quaternionic Variable. Journal of Approximation Theory. Vol.250 https://doi.org/10.1016/j.jat.2019.105325 ISSN: 0021-9045