Some applications of the trace condition for pluriharmonic functions in \(\mathbb{C}^n\) (Q1595454)

Two boundary value problems are under consideration: the classical Neumann problem for pluriharmonic functions in a smoothly bounded domain \(D\) of \(\mathbb{C}^n\), and the \(\overline\partial\)-problem \(\overline\partial u=f\) on \(D\) with the boundary condition \(\text{Re }u= g\). The existence of solutions is characterized in terms of orthogonality of the data to suitably chosen spaces of functions. In the case when \(D\) is the unit ball, the conditions can be expressed in terms of spherical harmonics.