On the zeros of a quaternionic polynomial: An extension of the Eneström-Kakeya theorem

Abdullah Mir

Czechoslovak Mathematical Journal (2023)

  • Volume: 73, Issue: 3, page 649-662
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Mir, Abdullah. "On the zeros of a quaternionic polynomial: An extension of the Eneström-Kakeya theorem." Czechoslovak Mathematical Journal 73.3 (2023): 649-662. <http://eudml.org/doc/299108>.

@article{Mir2023,
abstract = {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.},
author = {Mir, Abdullah},
journal = {Czechoslovak Mathematical Journal},
keywords = {quaternionic polynomial; Eneström-Kakeya theorem; zero-sets of a regular product},
language = {eng},
number = {3},
pages = {649-662},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the zeros of a quaternionic polynomial: An extension of the Eneström-Kakeya theorem},
url = {http://eudml.org/doc/299108},
volume = {73},
year = {2023},
}

TY - JOUR
AU - Mir, Abdullah
TI - On the zeros of a quaternionic polynomial: An extension of the Eneström-Kakeya theorem
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 3
SP - 649
EP - 662
AB - 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.
LA - eng
KW - quaternionic polynomial; Eneström-Kakeya theorem; zero-sets of a regular product
UR - http://eudml.org/doc/299108
ER -

References

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