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Vekua-Type Systems Related to Two-Sided Dual k-Hypermonogenic Functions

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Abstract

The aim of this paper is to solve the generalized Cauchy–Riemann systems of two-sided dual k-hypermonogenic functions, and to provide characterizations of the two-sided dual k-hypermonogenic functions. In this paper, we suggest a refinement for the definition of dual k-hypermonogenic functions by introducing left and right dual k-hypermonogenic operators. The new version of this definition is equivalent to the usual one which was introduced by Eriksson (Hypermonogenic functions and their dual functions, Birkhäuser, Basel, 2008), and it better adapts to the properties of dual k-hypermonogenic functions.

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Acknowledgements

The authors of the paper would like to express grateful thanks to the anonymous reviewers for their pfessional comments and suggestions, which are greatly helpful to improve the quality of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Guangdong University of Education, Guangzhou, 510303, China

    Kaili He

  2. Department of Basic Course Teaching, Software Engineering Institute of Guangzhou, Guangzhou, 510990, China

    Jianxun He

  3. School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, China

    Kaili He, Jianxun He, Zhenzhen Lou & Fusheng Xiao

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  1. Kaili He
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  2. Jianxun He
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  3. Zhenzhen Lou
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  4. Fusheng Xiao
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Correspondence to Jianxun He.

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Communicated by Wolfgang Sproessig.

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The first author was supported by the Innovation Research for the Postgraduates of Guangzhou University (Grant No. 2020GDJC-D06); The research was supported by the National Natural Science Foundation of China (Grant No. 12071229); This work was supported by the Project of Guangzhou Science and Technology Bureau (Grant No. 202102010402). This article is part of the topical collection “Higher Dimensional Geometric Function Theory and Hypercomplex Analysis” edited by Irene Sabadini, Michael Shapiro and Daniele Struppa.

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He, K., He, J., Lou, Z. et al. Vekua-Type Systems Related to Two-Sided Dual k-Hypermonogenic Functions. Complex Anal. Oper. Theory 16, 106 (2022). https://doi.org/10.1007/s11785-022-01270-3

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  • DOI: https://doi.org/10.1007/s11785-022-01270-3

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