scholarly journals Evaluation schemes in the ring of quaternionic polynomials

2017 ◽  
Vol 58 (1) ◽  
pp. 51-72 ◽  
Author(s):  
M. Irene Falcão ◽  
Fernando Miranda ◽  
Ricardo Severino ◽  
M. Joana Soares
Keyword(s):  
Quaternionic Polynomials

scholarly journals Almansi Theorem and Mean Value Formula for Quaternionic Slice-regular Functions

2020 ◽  
Vol 30 (4) ◽  
Author(s):  
Alessandro Perotti
Keyword(s):  
Harmonic Functions ◽  
Mean Value ◽  
Zonal Harmonic ◽  
Slice Regular Functions ◽  
Regular Functions ◽  
Quaternionic Polynomials ◽  
Mean Value Formula

Abstract We prove an Almansi Theorem for quaternionic polynomials and extend it to quaternionic slice-regular functions. We associate to every such function f, a pair $$h_1$$ h 1 , $$h_2$$ h 2 of zonal harmonic functions such that $$f=h_1-\bar{x} h_2$$ f = h 1 - x ¯ h 2 . We apply this result to get mean value formulas and Poisson formulas for slice-regular quaternionic functions.

scholarly journals A Note on the Computation of All Zeros of Simple Quaternionic Polynomials

2010 ◽  
Vol 48 (1) ◽  
pp. 244-256 ◽  
Author(s):  
Drahoslava Janovská ◽  
Gerhard Opfer
Keyword(s):  
Quaternionic Polynomials

The existence of left eigenvalues for quaternionic matrix

2021 ◽  
pp. 2250207
Author(s):  
Yan Yang ◽  
Kit Ian Kou
Keyword(s):  
Rational Functions ◽  
Algebraic Method ◽  
Quaternionic Matrix ◽  
Quaternionic Polynomials

In this work, an algebraic method to prove the existence of left eigenvalues for the quaternionic matrix is investigated. The left eigenvalues of a [Formula: see text] quaternionic matrix can be derived by solving the zeros of a general quaternionic polynomial of degree [Formula: see text]. Using the Study’s determinant, it can be found by solving the zeros of quaternionic polynomials of degree at most [Formula: see text] or of rational functions.

Quadratic One Sided Quaternionic Polynomials

2009 ◽  
Author(s):  
Drahoslava Janovská ◽  
Gerhard Opfer ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Quaternionic Polynomials

scholarly journals Mathematica Tools for Quaternionic Polynomials

2017 ◽  
pp. 394-408
Author(s):  
M. Irene Falcão ◽  
Fernando Miranda ◽  
Ricardo Severino ◽  
M. Joana Soares
Keyword(s):  
Quaternionic Polynomials

scholarly journals Computations in the ring of quaternionic polynomials

2010 ◽  
Vol 45 (1) ◽  
pp. 38-45 ◽  
Author(s):  
Alberto Damiano ◽  
Graziano Gentili ◽  
Daniele Struppa
Keyword(s):  
Quaternionic Polynomials

scholarly journals Quaternionic polynomials with multiple zeros: A numerical point of view

2017 ◽  
Author(s):  
M. I. Falcão ◽  
F. Miranda ◽  
R. Severino ◽  
M. J. Soares
Keyword(s):  
Point Of View ◽  
Multiple Zeros ◽  
Quaternionic Polynomials
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