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2012 On the Differentiability of Quaternion Functions
Omar Dzagnidze
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Tbilisi Math. J. 5(1): 1-15 (2012). DOI: 10.32513/tbilisi/1528768885

Abstract

Motivated by the general problem of extending the classical theory of holomorphic functions of a complex variable to the case of quaternion functions, we give a notion of an $\mathbb{H}$-derivative for functions of one quaternion variable. We show that the elementary quaternion functions introduced by Hamilton as well as the quaternion logarithm function possess such a derivative. We conclude by establishing rules for calculating $\mathbb{H}$-derivatives.

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Omar Dzagnidze. "On the Differentiability of Quaternion Functions." Tbilisi Math. J. 5 (1) 1 - 15, 2012. https://doi.org/10.32513/tbilisi/1528768885

Information

Received: 3 May 2011; Revised: 27 March 2012; Accepted: 2 April 2012; Published: 2012
First available in Project Euclid: 12 June 2018

zbMATH: 1280.30022
MathSciNet: MR2950182
Digital Object Identifier: 10.32513/tbilisi/1528768885

Subjects:
Primary: 30G35‎
Secondary: 30A05, 30B10

Rights: Copyright © 2012 Tbilisi Centre for Mathematical Sciences

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Vol.5 • No. 1 • 2012
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