Czechoslovak Mathematical Journal, first online, pp. 1-17


On representations of real analytic functions by monogenic functions

Hongfen Yuan

Received December 15, 2017.   Published online April 15, 2019.

Abstract:  Using the method of normalized systems of functions, we study one representation of real analytic functions by monogenic functions (i.e., solutions of Dirac equations), which is an Almansi's formula of infinite order. As applications of the representation, we construct solutions of the inhomogeneous Dirac and poly-Dirac equations in Clifford analysis.
Keywords:  monogenic function; inhomogeneous Dirac equation; inhomogeneous poly-Dirac equation; Almansi's formula of infinite order; Clifford analysis
Classification MSC:  30G35, 35J05, 35C10
DOI:  10.21136/CMJ.2019.0573-17

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Affiliations:   Hongfen Yuan, School of Mathematics and Physics, Hebei University of Engineering, Guangming South Street 199, Handan, Hebei Prov., 056038, P. R. China, e-mail: yhf0609@163.com


 
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