Monogenic and Holomorphic Functions

Abstract

The theory of holomorphic functions of several variables and the theory of monogenic functions (Clifford-analytic functions) are similar in the following sense. We write \({C^m} = {R^m} \oplus i{R^m}\) and \({R^{m + 1}} = {R^m} \oplus R\) Let f be a real-valued, real analytic function defined in an open subset of \({R^m}\) f may be extended to a holomorphic function on an open subset of C m or to a monogenic function on an open set of R m+1; roughly speaking the knowledge of the latter is equivalent of the knowledge of the former. This motivates an explicit change from a holomorphic function to a monogenic function.