Quaternionic k-Hyperbolic Derivative

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Eriksson , S-L & Orelma , H 2017 , ' Quaternionic k-Hyperbolic Derivative ' , Complex Analysis and Operator Theory , vol. 11 , no. 5 , pp. 1193-1204 . https://doi.org/10.1007/s11785-016-0630-8

Title: Quaternionic k-Hyperbolic Derivative
Author: Eriksson, Sirkka-Liisa; Orelma, Heikki
Contributor organization: Department of Mathematics and Statistics
Date: 2017-06
Language: eng
Number of pages: 12
Belongs to series: Complex Analysis and Operator Theory
ISSN: 1661-8254
DOI: https://doi.org/10.1007/s11785-016-0630-8
URI: http://hdl.handle.net/10138/307308
Abstract: 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 ds(2) = dx(0)(2) + dx(1)(2) + dx(2)(2)/x(2)(2k) 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.
Subject: k-Hypermonogenic
Hyperbolic metric
Hyperbolic Laplace
111 Mathematics
Peer reviewed: Yes
Usage restriction: openAccess
Self-archived version: acceptedVersion

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