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Keywords:
quaternionic polynomial; Eneström-Kakeya theorem; zero-sets of a regular product
quaternionic polynomial; Eneström-Kakeya theorem; zero-sets of a regular product
Summary:
We present some results on the location of zeros of regular polynomials of a quaternionic variable. We derive new bounds of Eneström-Kakeya type for the zeros of these polynomials by virtue of a maximum modulus theorem and the structure of the zero sets of a regular product established in the newly developed theory of regular functions and polynomials of a quaternionic variable. Our results extend some classical results from complex to the quaternionic setting as well.
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