A Goursat Decomposition for Polyharmonic Functions in Euclidean Space

Abstract

The Goursat representation formula in the complex plane, expressing a real-valued biharmonic function in terms of two holomorphic functions and their anti-holomorphic complex conjugates, is generalized to Euclidean space, expressing a real-valued polyharmonic function of order p in terms of p the so called monogenic functions of Clifford analysis.

Keywords

• Goursat decomposition
• polyharmonic function