Geodesic
Zeros of one class of quaternionic polynomials
Filomat, Tome 36 (2022) no. 19, p. 6655

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DOI

The goal of this paper is to study the properties of zeros of some special quaternionic polynomials with restricted coefficients, namely coefficients whose real and imaginary components satisfy suitable inequalities. We extend the well-known Eneström-Kakeya theorem and its various generalizations from complex to the quaternionic setting. The main tools used to derive the bounds for the zeros of these polynomials are the maximum modulus theorem and the structure of the zero sets established in the newly developed theory of regular functions and polynomials of a quaternionic variable.
DOI : 10.2298/FIL2219655M
Classification : 30E10, 30G35, 16K20
Keywords: Holomorphic functions, Quaternionic polynomials, Eneström-Kakeya theorem, Zero-sets of a regular function 
Gradimir V Milovanović; Abdullah Mir. Zeros of one class of quaternionic polynomials. Filomat, Tome 36 (2022) no. 19, p. 6655 . doi: 10.2298/FIL2219655M
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     author = {Gradimir V Milovanovi\'c and Abdullah Mir},
     title = {Zeros of one class of quaternionic polynomials},
     journal = {Filomat},
     pages = {6655 },
     year = {2022},
     volume = {36},
     number = {19},
     doi = {10.2298/FIL2219655M},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2219655M/}
}
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