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\(\varvec{(m,h)}\)-Monogenic Functions Related to Axially Symmetric Helmholtz Equations

  • Doan Cong DinhEmail author
Article
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Abstract

In this paper we introduce a new type of Vekua’s equation in Clifford analysis. There are two directions of this topic: The theory of h-regular functions was investigated by E. Obolashvili and the theory k-hypermonogenic functions has been developed by H. Leutwiler, S.-L. Eriksson and their co-workers. These two theories are investigated independently. We introduce a combination of them in a united form.

Keywords

Clifford analysis h-regular functions k-hypermonogenic functions Generalized monogenic functions Generalized Cauchy kernel Integral representation of solutions Axially symmetric Helmholtz equation 

Mathematics Subject Classification

30A05 30G30 30G35 15A66 35A08 

Notes

Acknowledgements

The author would like to express his sincere gratitude to the Anonymous Referees for their useful comments to improve this paper.

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Authors and Affiliations

  1. 1.School of Applied Mathematics and InformaticsHanoi University of Science and TechnologyHanoiVietnam

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