Representation of an infinitely differentiable function by a difference of plurisubharmonic functions (Q1091513)

Let u be a real valued, \({\mathcal C}^{\infty}\)-function defined on \({\mathbb{C}}^ n\). The main theorem of the paper states, that there exist plurisubharmonic functions \(u_ 1\) and \(u_ 2\) and a pluriharmonic function h such that \(u=u_ 1-u_ 2+h\) in \({\mathbb{C}}^ n\). Furthermore one can find non-negative Borel measures \(\mu_ 1\), \(\mu_ 2\) on \({\mathbb{C}}^{n+1}\) such that \(u_ j(z)=\int \ln | s-<z,w>| d\mu_ j(s,w)\), where \(j=1,2\). See also the author [Mat. Zametki 36, No.6, 865-871 (1984; Zbl 0563.31005)].