Quaternionic Clifford Analysis: The Hermitian Setting

Abstract.

In this paper we introduce the quaternionic Witt basis in ${\mathbb{R}_m=\mathbb{H}\otimes_{\mathbb{R}}\mathbb{R}+m, m=4n}$. We then define a notion of quaternionic hermitian vector derivative which leads to hermitian monogenic functions. We study the resolutions associated to quaternionic hermitian systems in the 4 and 8 dimensional cases. We finally prove Martinelli–Bochner type formulae.

Communicated by Daniel Alpay.