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The pluriharmonic problem in a spherical domain of ${\bbfC}\sp n$ for n$\ge 3$. (Italian. English summary) Zbl 0577.32017
The author presents a finite collection of explicit second order linear partial differential operators on the boundary $b\Omega$ of the unit ball $\Omega$ in ${\bbfC}\sp n$, such that the corresponding homogeneous system of PDE characterizes the boundary values of pluriharmonic functions on $\Omega$, provided $n\ge 3$. The result has also a local version. Similar results were found earlier by {\it T. Audibert} [C.R. Acad. Sci., Paris, Sér. A 284, 1029-1031 (1977; Zbl 0346.31004)] and {\it M. Nacinovich} [Complex analysis, Proc. Summer Sch., Trieste 1980, Lect. Notes Math. 950, 105-195 (1982; Zbl 0513.32029)].
Reviewer: R.M.Range
##### MSC:
 32U05 Plurisubharmonic functions and generalizations 31C10 Pluriharmonic and plurisubharmonic functions 35G05 General theory of linear higher-order PDE
##### Keywords:
boundary values of pluriharmonic functions