On the Structure of the Set of Zeros of Quaternionic Polynomials

By A. Pogorui *, M. Shapiro. 2004

114 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4fdd5a352832b45cd8679008196b356139355e1b

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Regular Functions of a Quaternionic Variable (2013, background): “In Chapter 3, we survey the study of the zero sets conducted in [23, 24, 30, 31], which extended [45, 46] (see also [17, 34]).”
Regular Moebius transformations of the space of quaternions (2008, background): “For n > 1, by the fundamental theorem of algebra for quaternions (see, for instance, [10, 16, 18, 19]), qan + .”
Slice regular functions on real alternative algebras (2010, methodology): “This estimate was improved on the quaternions by Pogorui and Shapiro [30]: if p has s spherical zeros and l non–spherical zeros, then 2s + l ≤ m. Gentili and Struppa [20] showed that, using the right definition of multiplicity, the number of zeros of p equals the degree of the polynomial.”
Zeros of regular functions and polynomials of a quaternionic variable (2008, methodology): “We will rephrase here the interesting proof given in [12].”
A new series expansion for slice regular functions (2011, background): “After the study of the roots of polynomials of [17], the following result was proven for power series in [7], and in the following form in [9] (for generalizations to other real alternative algebras, see [13, 14]).”
On the Multiplicity of Zeroes of Polynomials with Quaternionic Coefficients (2008, background): “This is not surprising since, as pointed out in [ 6 ], the problem of dening a good notion of multiplicity for zeroes of quaternionic polynomials is a rather complicated question.”
The fundamental theorem of algebra for Hamilton and Cayley numbers (2008, methodology): “1 and what is proved in [11] for the case of quaternions directly lead to the following simple description of zero sets of regular polynomials.”
A New Theory of Regular Functions of a Quaternionic Variable (2007, background): “At the beginning of this last section, we prove a result which extends to the case of power series an earlier result of Pogorui and Shapiro (see [11]).”
Regular Functions on the Space of Cayley Numbers (2010, result): “Finally, we are able to describe the zeroes of regular functions, with a result inspired by [ 18 ].”