Quaternionic G–Monogenic Mappings in Em

Shpakivskyi, V. S. and Kuzmenko, T. S. (2018) Quaternionic G–Monogenic Mappings in Em. International Journal of Advanced Research in Mathematics, 12. pp. 1-34. ISSN 2297-6213

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Abstract

We consider a class of so-called quaternionic G-monogenic mappings associated with m-dimensional (m 2 f2; 3; 4g) partial differential equations and propose a description of all mappings from this class by using four analytic functions of complex variable. For G-monogenic mappings we generalize some analogues of classical integral theorems of the holomorphic function theory of the complex variable (the surface and the curvilinear Cauchy integral theorems, the Cauchy integral formula, the Morera theorem), and Taylor’s and Laurent’s expansions. Moreover, we investigated the relation between G-monogenic and H-monogenic (differentiable in the sense of Hausdorff) quaternionic mappings.

Item Type: Article
Uncontrolled Keywords: complex quaternions algebra, Gâteaux derivative, G-monogenic mappings, constructive description, integral theorems, Taylor’s and Laurent’s expansions, singular points, H-monogenic mappings.
Subjects: Q Science > QA Mathematics > Mathematical Analysis
Divisions: Faculty of Physics and Mathematics > Department of Mathematical Analysis
Depositing User: Ірина Ігорівна Таргонська
Date Deposited: 04 Mar 2019 10:48
Last Modified: 04 Mar 2019 10:48
URI: http://eprints.zu.edu.ua/id/eprint/28514

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