Abstract:
For any multifunction S⊂Dz×Cw, we give a criterion for analyticity (pseudoconcavity) in terms of plurisubharmonicity of the function V(z,w)=−lnρ(w,Sz), where ρ(w,Sa) stands for the distance from the point w to the set Sa=S∩{z=a}.
Keywords:
analytic multifunction, subharmonic function, pseudoconcavity, pseudoconvexity, plurisubharmonicity, pluripolarity, capacity of a set, Hartogs series.