Regular quaternionic polynomials and their properties
| Autor: | Yu. M. Grigor’ev |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Numerical Analysis
Mathematics::Complex Variables Applied Mathematics Discrete orthogonal polynomials 010102 general mathematics Hypercomplex analysis 01 natural sciences Classical orthogonal polynomials Algebra Computational Mathematics Difference polynomials 0103 physical sciences Wilson polynomials Orthogonal polynomials Elementary symmetric polynomial 010307 mathematical physics 0101 mathematics Ring of symmetric functions Analysis Mathematics |
| Zdroj: | Complex Variables and Elliptic Equations. 62:1343-1363 |
| ISSN: | 1747-6941 1747-6933 |
| DOI: | 10.1080/17476933.2016.1250877 |
| Popis: | Unlike in complex analysis, in all hypercomplex function theories a hypercomplex variable is not monogenic (regular) and there exists a problem to define analogues of positive and negative powers of the complex variable. R. Fueter firstly introduces a system of symmetric regular quaternion polynomials as analogues of positive powers of a complex variable and proves the Taylor theorem in his theory. In Clifford analysis an analogical idea is used. The Fueter symmetric polynomials are both left- and right-regular, the symmetric polynomials in Clifford analysis are also both left- and right-monogenic. In this paper we construct only left-regular quaternion polynomials and show that the theory of regular quaternion functions of a vector valued quaternion variable can be developed using these polynomials. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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