Holomorphic functions on the lie ball and their monogenic counterparts

Abstract

The Cauchy integral formula in Clifford analysis allows us to associate a holomorphic function $\tilde f:L_n\to \C$ on the Lie ball $L_n$ in $\C^n$ with its monogenic counterpart $f:B_1(0)\to \C^{n+1}$ via the formula $\tilde f(z) = \int_{S^n}G_\om(z)\bs n(\om)f(\om)\,dμ(\om)$, $z\in L_n.$ The inverse map $\tilde{f}\mapsto f$ is constructed here using the Cauchy-Hua formula for the Lie ball following the work of M. Morimoto \cite{Mori2}.