Complex k-hypermonogenic functions in complex Clifford analysis

Abstract

First, we consider the relationships between complex k-hypermonogenic functions and complex monogenic functions. Then we discuss necessary and sufficient conditions for complex k-hypermonogenic functions which is similar to the Cauchy–Riemann equation. Finally, we establish three theorems about complex partial differential equations.

Keywords:

• complex k-hypermonogenic functions
• H _k solution
• complex Clifford analysis

AMS Subject Classifications::

• 30B30
• 31B10

Acknowledgements

This work was supported by the National Science Foundation of China (Grant No. 10771049), the Science Foundation of Hebei Province (A2010000351, A2010000346) and the Foundation of Hebei Normal University (L2009y02).