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On Structure of Inframonogenic Functions

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Abstract

This paper deals with the inframonogenic functions which are solutions of the sandwich equation \(DfD=0\), where D is the Dirac operator in \({\mathbb {R}}^n\). The inframonogenic functions plays an important role in Fischer decomposition for homogeneous polynomials and applications in elasticity theory. In this paper we introduce a general structure of the inframonogenic functions in star-like domains in the form

$$\begin{aligned} f(x)=h(x)+2g(x)x+|x|^2 \cdot gD(x), \end{aligned}$$

where g and h are, respectively, left and right monogenic functions.

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Acknowledgements

The author would like to express his sincere gratitude and esteem to the Editors and the Reviewers for their consideration of this paper. This research is funded by Hanoi University of Science and Technology (HUST) under Grant number T2020-PC-301.

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  1. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam

    Doan Cong Dinh

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  1. Doan Cong Dinh
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Correspondence to Doan Cong Dinh.

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Communicated by Wolfgang Sprössig.

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Dinh, D.C. On Structure of Inframonogenic Functions. Adv. Appl. Clifford Algebras 31, 50 (2021). https://doi.org/10.1007/s00006-021-01157-0

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