The author presents a finite collection of explicit second order linear partial differential operators on the boundary of the unit ball in , such that the corresponding homogeneous system of PDE characterizes the boundary values of pluriharmonic functions on , provided . The result has also a local version.
Similar results were found earlier by T. Audibert [C.R. Acad. Sci., Paris, Sér. A 284, 1029-1031 (1977; Zbl 0346.31004)] and M. Nacinovich [Complex analysis, Proc. Summer Sch., Trieste 1980, Lect. Notes Math. 950, 105-195 (1982; Zbl 0513.32029)].