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.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-10421 |
| Date | 01 February 2020 |
| Creators | Carney, N., Gardner, Robert B., Keaton, R., Powers, A. |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Source | ETSU Faculty Works |
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