Quaternionic k-Hyperbolic Derivative
| Autor: | Heikki Orelma, Sirkka-Liisa Eriksson |
|---|---|
| Přispěvatelé: | Department of Mathematics and Statistics |
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Monogenic Laplace-Beltrami Differential form Holomorphic function k-Hypermonogenic 01 natural sciences chemistry.chemical_compound HYPERMONOGENIC FUNCTIONS 0103 physical sciences 111 Mathematics 0101 mathematics Quaternion Hyperbolic Laplace Mathematics Hypercomplex number Hyperbolic metric Applied Mathematics 010102 general mathematics Mathematical analysis Operator theory Computational Mathematics Computational Theory and Mathematics chemistry k-Hyperbolic Partial derivative 010307 mathematical physics Quaternions Derivative (chemistry) |
| Zdroj: | Complex Analysis and Operator Theory. 11:1193-1204 |
| ISSN: | 1661-8262 1661-8254 |
| DOI: | 10.1007/s11785-016-0630-8 |
| Popis: | Complex holomorphic functions are defined using a complex derivative. In higher dimensions the meaningful generalization of complex derivative is not straight forward. Sudbery defined a derivative for quaternion regular functions using differential forms. Gurlebeck and Malonek generalized that for monogenic functions. In this paper we find similar characterizations for k-hypermonogenic functions which are holomorphic functions based on the Riemannian metric $$\begin{aligned} ds^{2}=\frac{dx_{0}^{2}+dx_{1}^{2}+dx_{2}^{2}}{x_{2}^{2k}}. \end{aligned}$$ When \(k=0\), we obtain the hypercomplex derivative by Gurlebeck and Malonek. Just like in the complex case derivative of k-hypermonogenic is the usual partial derivative with respect to the first coordinate. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink