Traces of pluriharmonic functions on curves
Let \(B_ n\) be the unit ball in \(C^ n\), S its boundary, and \(\gamma\) a simple smooth curve in S; it is well known that \(\gamma\) is an interpolation set for the ball algebra (that is every continuous function on \(\gamma\) is the restriction of a function holomorphic in \(B_ n\) and continuous on \(\bar B_ n)\) if and only if at each point of \(\gamma\), the tangent vector lies in the complex tangent space of S at that point. A subset E of S is said to be a set of pluriharmonic (resp. almost pluriharmonic) interpolation if any continuous function on E can be extended to a pluriharmonic function continuous on \(\bar B_ n\) (resp. the space of the restrictions of continuous pluriharmonic functions on \(\bar B_ n\) to E is of finite-codimension in the space of continuous functions on E). The authors' main result is to show that a smooth simple closed curve in S is of almost pluriharmonic interpolation.
scientific article; zbMATH DE number 4200580