Let Ω = \left{ {ρ < 0} \
ight} be a domain with {C^3}-boundary Γ = \left{ {ρ = 0} \
ight}. For a large class of domains, the functions u \in {C^3}(Γ ) which are the restrictions of pluriharmonic functions on Ω are characterized as the solutions of a system of partial differential equations.
