Holomorphic synthesis of monogenic functions of several quaternionic variables
Let \(\Sigma\) be the variety of complex structures \(\sigma\) in the quaternions \(H\) which make \(H\) isomorphic to \(C^{2}\) and which are consistent with the metric and orientation in \(H\). It is proved that \(\Sigma\) is isomorphic to the manifold of all proper ideals in the complexified quaternion algebra \(H_{C}\). This enables the author to find a representation for polymonogenic functions in \(H\) by integrating over \(\Sigma\). Here polymonogenic means functions which are monogenic to each of several quaternionic variables. See also \textit{W. W. Adams, P. Loustaunau, V. P. Palamodov} and \textit{D. C. Struppa} in Ann. Inst. Fourier 47, No. 2, 623-640 (1997; Zbl 0974.32005).
scientific article; zbMATH DE number 1369960