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)\,d\mu(\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}