Integral formula of isotonic functions over unbounded domain in Clifford analysis
The author considers an isotonic Dirac system in a class of very general unbounded domains in \(\mathbb{R}^n\) \((n= 2k)\). Such a system can be described by \[ D_{x_1} f(x)+ i\widetilde f(x)D_{x_2}, \] where \(x_1= \sum_{j=1} 1me_i x_i\), \(x_2= \sum^m_{j=1} e_j x_{m+j}\) and \(D_{x_i}\) \((i= 1,2)\) are the corresponding Dirac operators. Borel-Pompeiu's integral formula is obtained. A relation to the Hermitean monogeneity is deduced. The author finds a formula of Martinelli-Bochner type over this class of domains.
scientific article; zbMATH DE number 5695459